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Full text of "What Is Science"

THE BOOK WAS 
DRENCHED 



OU_168067>3 



OSMANIA 19N1VERSITY LIBRARY 

Oal1 No - ? Accession No, 3fc& TS~ 




Title 



This book should be returned on or before the date last marked below. 



WHAT 

IS SCIENCE? 

TWELVE EMINENT SCIENTISTS 
AND PHILOSOPHERS EXPLAIN 
THEIR VARIOUS FIELDS 
TO THE LAYMAN 

Edited by James R. Newman 




SIMON AND SCHUSTER 
NEW YORK * 1955 



ALL RIGHTS RESERVED 

INCLUDING THE RIGHT OF REPRODUCTION 
IN WHOLE OR IN PART IN ANY FORM 
COPYRIGHT, , 1955, BY JAMES R. NEWMAN 
PUBLISHED BY SIMON AND SCHUSTER, INC. 
ROCKEFELLER CENTER, 630 FIFTH AVENUE 
NEW YORK 20, N. Y. 

THIRD PRINTING 

LIBRARY OF CONGRESS CATALOG CARD NUMBER: 55-11042 
MANUFACTURED IN THE UNITED STATES OF AMERICA 
BY H. WOLFF BOOK MFG. CO., INC., NEW YORK 



Contents 



INTRODUCTION James R. Newman vii 

SCIENCE AND HUMAN LIFE Bert rand Russell 6 

MATHEMATICS AND LOGIC Sir Edmund Taylor Whittaker 

ASTRONOMY AND COSMOLOGY Hermann Bondi 66 

PHYSICS Edward U. Condon 102 

CHEMISTRY John Read 154 

BIOCHEMISTRY Ernest Baldwin 198 

BIOLOGY Warder Clyde Alice 231 

EVOLUTION AND GENETICS Julian Huxley 256 

PSYCHOLOGY Edwin G. Boring 294 

ANTHROPOLOGY Clyde Kluckhohn 319 

PSYCHOANALYSIS Erich Fromm 362 

SCIENCE AS FORESIGHT Jacob Bronowski 385 

Bibliography 437 

Index 459 



Introduction 



Twelve scientists and philosophers have contributed freshly written 
essays to this symposium on science and the scientific outlook. The 
book is addressed to the general reader. 

There is no want of literature on what science has done, or is ex- 
pected to do tomorrow, to increase man's control over nature. While 
these achievements and hopes are discussed in the present volume, 
they are not its principal concern. Its emphasis is rather on the nature 
of scientific knowledge, on the scientific method, on science as an 
intellectual pursuit; in short, the book attempts to answer the 
question: What is science? Another matter examined in these pages 
is the bearing of science on society. It is a commonplace that science 
is not wisdom; that it may save us from the pox but not from our own 
folly. But like many other commonplaces this one is not very helpful. 
Indeed, it is a source of much mischief because it promotes the cause 
of fashionable philosophies which assert that, since science cannot 
provide answers for all human problems, it is not a safe guide in deal- 
ing with any of them. We all agree that science has changed civiliza- 
tion and will continue to change it if there is a civilization left. But 
we do not agree and on this point scientists no less than other 
thoughtful men fall out among themselves as to how knowledge can 
be used for good ends and what are the responsibilities of its dis- 
coverers to see that it is not used for bad ends. Science cannot resolve 
these issues but scientists have no right to evade them. Several of the 
authors of this symposium have dealt with the subject at length; Lord 
Russell has devoted his entire essay to it. 

vti 



viii Introduction 

Though -written for persons without special training, the pieces in 
this book are not always easy. Neither is modern science. A decent 
respect for the reader requires that he be told when a subject admits 
of no further simplification; the contributors, I am glad to say, have 
not pretended to explain what cannot here be explained. Neverthe- 
less, every effort has been made to speak plainly, to refrain from 
jargon and nebulous profundities, to enlighten rather than to astound. 
Although some areas are too difficult for any deep explorations in 
these pages, the nature of the problem, the aims of its investigators 
and the instruments they use, have been made clear. Thus if it has 
not always been possible to escort him through it, the reader has at 
least been given many fresh and exciting glimpses of the promised 
land. 

Some of the contributors provided abundant material for the prep- 
aration of biographical sketches and lists of suggested readings. In 
other instances, especially where the authors have been excessively 
self-effacing, I have had to rely upon the biographical scraps of con- 
ventional reference books which have not always been very lively or 
illuminating. I wish to express my appreciation for the valuable edi- 
torial assistance of my old friend and associate Robert Hatch. I am 
most thankful for help generously given by Dr. J. Bronowski and 
Professor Ernest Nagel. 

The authors of this book have succeeded, I believe, in giving an 
unusually rich and illuminating picture of scientific thinking. They 
have offered thoughtful opinions on the possibilities and the limita- 
tions of science, what it can contribute to civilization and what other 
ingredients are required to assure the progress or perhaps one should 
say, survival of society. I hope this book helps to a more balanced 
view both of science and human values. I hope it helps counteract 
the malicious doctrines, flourishing again in this age of insecurity, 
which belittle science and reason, exhort men to consult their hearts 
instead of their heads, depreciate the lessons of experience and pro- 
claim the higher truth emanating from inner voices. "Science," said 
Adam Smith, "is the great antidote to the poison of enthusiasm and 
superstition!' An ailing world would do well to reach for the right 
bottle in the medicine cabinet 

JAMES R. NEWMAN 



SCIENCE AND 
HUMAN LIFE 

BERTRAND RUSSELL 



about 

Bertrand Russell 



Bertrand Arthur William Russell was born at Trelleck, in Mon- 
mouthshire, England on May 18, 1872. His father was Viscount 
Amberley, his mother, Kate Stanley, daughter of Baron Stanley of 
Alderley. Both parents died before Russell was four years old and he 
was brought up by his grandmother, Countess Russell, a woman of 
strong opinions and puritanical principles. Her elevated outlook on 
social matters, her indifference to money "only possible" as Russell 
says, "to those who have always had it' 9 and to other conventional 
earmarks of success, her "belief in private judgment and the suprem- 
acy of the individual conscience" all had a profound influence on 
the formation of Russell's character. 

Russell was tutored at home until he was 18; he then went to 
Cambridge where he concentrated on mathematics and philosophy. 
Among his teachers was Alfred North Whitehead who played a cen- 
tral part in the younger man's mental development, became his 
friend and later collaborated with him in the writing of the Principia 
Mathematica, one of the great intellectual achievements of the twen- 
tieth century. 

After graduating from Cambridge Russell spent several years 
abroad, visited America in 1896, and in 1898 returned to Trinity 
College, Cambridge, as a lecturer and fellow. His first book, German 
Social Democracy, appeared in 1896; other early writings include An 
Essay on the Foundations of Geometry (1897) and his admirable 



about Bertrand Russell 3 

monograph, A Critical Exposition of the Philosophy of Leibniz 
(1900). 

Russell describes 1900 as "the most important year in my intellec- 
tual life!' He 'went that year -with Whitehead to the International 
Congress of Philosophy in Paris where he listened to the Italian logi- 
cian Peano give an account of his system of symbolic logic. This ex- 
perience stimulated Russell's own interest in the field and led to two 
of his major works, The Principles of Mathematics (1903) and the 
Principia Mathematica (1910-1913). 

Although RusselVs primary interests for many years were philoso- 
phy and the foundations of mathematics, he was at all times deeply 
concerned with politics and the problems of society. He was active in 
that famous organization for the advancement of socialism, the Fa- 
bian Society, and was a close friend of Sidney and Beatrice Webb. At 
one time he considered standing for Parliament, but because he de- 
clined to conceal his agnosticism could not win party support for his 
candidacy. An outspoken opposition to conscription brought him into 
difficulties during the First World War. He was fined and dismissed 
from his college post. In 1918 he was imprisoned for six months be- 
cause he had written a pamphlet accusing the American Army of "m- 
timidating strikers' at home, which was regarded as "likely to preju- 
dice His Majesty's relations with the United States of America." 
While in jail he wrote his Introduction to Mathematical Philosophy, 
first published in 1919. By the time Russell was released the governor 
of the prison must have felt that he had had quite enough of mathe- 
matical philosophers: he had been required, though unable to com- 
prehend it, to read the manuscript of Russell's book for possible 
seditious tendencies. 

In 1920 Russell made a trip to Russia, where he met Lenin, 
Trotsky and Gorki. From this visit came The Practice and Theory of 
Bolshevism (1920), in which Russell praised the fundamental ideas 
of communism but warned against the excesses of those who held 
power and were determined at all costs to put the ideas into practice. 
He spent a year in China (1920-21), with whose people he devel- 
oped a close bond of sympathy. Looking back on this visit in 1943, 
he wrote: "I loved the Chinese, but it was obvious that the resistance 
to hostile militarisms must destroy much of what was best in then 



4 What Is Science? 

civilization. 97 After this trip he returned to teaching and lecturing in 
England and the United States. His voluminous writings on general 
questions brought his name to the attention of a wide audience. Be- 
tween 1920 and 1940 he published many books and more than 200 
articles on mathematical, philosophical, scientific, political and social 
subjects. No other contemporary philosopher ranged over so broad a 
field or stood so high in popular esteem. Among his principal works 
are Mysticism and Logic (1 91 8), a brilliant and eloquent collection of 
essays; The Analysis of Mind (1921); The Prospects of Industrial 
Civilization (1923), a study of socialism written in collaboration with 
his second wife, Dora Russell; The ABC of Relativity (1925); The 
Analysis of Matter (1927); An Outline of Philosophy (1927), perhaps 
the best of modern introductions to philosophical thought; Marriage 
and Morals (1929); The Scientific Outlook (1931); Education and the 
Social Order (1932); Freedom and Organization (1934); Power (1938), 
regarded as one of the most trenchant of analyses of the theory of the 
state; An Inquiry into Meaning and Truth (1940), the William James 
lectures at Harvard University; History of Western Philosophy (1946); 
Human Knowledge (1948); Unpopular Essays (1950); The Impact of 
Science on Society (1951); Human Society in Ethics and Politics 
(1955). 

Russell has made many visits to the United States, his longest stay 
being from 1938 to 1944. During this period he lectured at the Uni- 
versity of Chicago, at the University of California in Los Angeles, at 
Harvard and at the Barnes Foundation at Merion, Pennsylvania. He 
was appointed a professor of philosophy at the College of the City of 
New York, but the appointment was revoked by court order when an 
anguished lady brought suit to have the appointment annulled on the 
ground of Russell's "advocacy of free love!' On his return to England 
in 1944 Russell was again appointed to a fellowship at Trinity Col- 
lege. He continued to write, lecture and express himself vigorously on 
topics ranging from epistemology to the catastrophic consequences of 
modern warfare. He has received almost every distinction his country 
can award, including the Order of Merit, and in 1950 was awarded the 
Nobel prize in literature. Russell writes with such incandescent clar- 
ity, wit and incisiveness that, regardless of theme, all his works are 
literary achievements. 



about Bertrand Russell 5 

Russell is 83 years old and in excellent health. He 'writes "with as 
much sting as he did 60 years ago. He remains a magnificent non- 
conformist, kindly, tolerant and skeptical in outlook the values he 
has always cherished. "I should like" he said a couple of years ago f 
"to live another ten years, provided there is not another world war 
meanwhile. If there is, there will be something to be said for being 
dead." 

It is a privilege to bring to the readers of this book the words of 
one who in mind and spirit embodies the highest good of our civiliza- 
tion. 



SCIENCE AND HUMAN LIFE 

BERTRAND RUSSELL 



Science and the techniques to which it has given rise have changed 
human life during the last hundred and fifty years more than it had 
been changed since men took to agriculture, and the changes that are 
being wrought by science continue at an increasing speed. There is no 
sign of any new stability to be attained on some scientific plateau. On 
the contrary, there is every reason to think that the revolutionary pos- 
sibilities of science extend immeasurably beyond what has so far been 
realized. Can the human race adjust itself quickly enough to these 
vertiginous transformations, or will it, as innumerable former species 
have done, perish from lack of adaptability? The dinosaurs were, in 
their day, the lords of creation, and if there had been philosophers 
among them not one would have foreseen that the whole race might 
perish. But they became extinct because they could not adapt them- 
selves to a world without swamps. In the case of man and science, 
there is a wholly new factor, namely that man himself is creating the 
changes of environment to which he will have to adjust himself with 
unprecedented rapidity. But, although man through his scientific 
skill is the cause of the changes of environment, most of these changes 
are not willed by human beings. Although they come about through 
human agencies, they have, or at any rate have had so far, something 
of the inexorable inevitability of natural forces. Whether Nature dried 
up the swamps or men deliberately drained them, makes little differ- 
ence as regards the ultimate result. Whether men will be able to sur- 



Science and Human Life 7 

vive the changes of environment that their own skill has brought about 
is an open question. If the answer is in the affirmative, it will be 
known some day; if not, not. If the answer is to be in the affirmative, 
men will have to apply scientific ways of thinking to themselves and 
their institutions. They cannot continue to hope, as all politicians 
hitherto have, that in a world where everything has changed, the po- 
litical and social habits of the eighteenth century can remain inviolate. 
Not only will men of science have to grapple with the sciences that 
deal with man, but and this is a far more difficult matter they will 
have to persuade the world to listen to what they have discovered. If 
they cannot succeed in this difficult enterprise, man will destroy him- 
self by his halfway cleverness. I am told that, if he were out of the 
way, the future would lie with rats. I hope they will find it a pleasant 
world, but I am glad I shall not be there. 

But let us pass from these generalities to more specific questions. 

One of the most obvious problems raised by a scientific technique is 
that of the exhaustion of the soil and of raw materials. This subject 
has been much discussed, and some governments have actually taken 
some steps to prevent the denudation of the soil. But I doubt whether, 
as yet, the good done by these measures is outweighing the harm done 
in less careful regions. Food, however, is such an obvious necessity 
that the problem is bound to receive increasing attention as popula- 
tion pressure makes it more urgent. Whether this increased attention 
will do good or harm in the long run is, I fear, questionable. By a 
spendthrift use of fertilizers, food production in the present can be 
increased at the cost of food production in the future. Can you 
imagine a politician going to his constituents and saying: "Ladies and 
gentlemen, it is in your power to have abundance of food for the next 
thirty years, but the measures that will give you this abundance will 
cause scarcity for your grandchildren. I am therefore proposing meas- 
ures to insure frugality in the present in order to avoid famine in the 
somewhat distant future." Is it possible to believe that a politician 
who said this would win elections against one less addicted to fore- 
sight? I hardly think so, unless the general level of political intelli- 
gence and virtue can be very considerably increased. 

The question of raw materials is more difficult and complex than 
the question of food. The raw materials required at one stage of tech' 



8 What Is Science? 

nique are different from those required at another. It may be that by 
the time the world's supply of oil is exhausted, atomic power will have 
taken its place. But to this sort of process there is a limit, though not 
an easily assignable one. At present there is a race for uranium, and 
it would seem likely that before very long there will be no easily ac- 
cessible source of uranium. If, when that happens, the world has come 
to depend upon nuclear energy as its main source of power, the result 
may be devastating. All such speculations are of course very question- 
able, since new techniques may always make it possible to dispense 
with formerly necessary raw materials. But we cannot get away from 
the broad fact that we are living upon the world's capital of stored 
energy and are transforming the energy at a continually increasing 
rate into forms in which it cannot be utilized. Such a manner of life 
can hardly be stable, but must sooner or later bring the penalty that 
lies in wait for those who live on capital. 

In primitive times, when the human population of the globe was 
small, such problems did not arise. Agriculture, it is true, was prac- 
ticed in ways that exhausted the soil for a time, but there were usually 
new vacant lands available; and if there were not, the corpses of 
enemies sufficed as fertilizers. The system was "conservative" in the 
physicists' sense. That is to say, energy on the whole accumulated as 
fast as it was used. Now, this is not the case; and, so far as one can 
see, it will never be the case while scientific technique continues. 

All this however, you may say, is distant and doubtful: we have 
more pressing matters to consider. This is true, and I will proceed to 
consider some of them. 

The problem which most preoccupies the public mind at the pres- 
ent moment is that of scientific warfare. It has become evident that, 
if scientific skill is allowed free scope, the human race will be ex- 
terminated, if not in the next war, then in the next but one or the next 
but two at any rate at no very distant date. To this problem there are 
two possible reactions: there are those who say, "let us create social 
institutions which will make large-scale war impossible"; there are 
others who say, "let us not allow war to become too scientific. We can- 
not perhaps go back to bows and arrows, but let us at any rate agree 
with our enemies that, if we fight them, both sides will fight ineffi- 
ciently/' For my part, I favor the former answer, since I cannot see 



Science and Human Life 9 

that either side could be expected to observe an agreement not to use 
modern weapons if once war had broken out. It is on this ground that 
I do not think that there will long continue to be human beings unless 
methods are found of permanently preventing large-scale wars. But 
this is a serious question as to which I will say no more at the moment. 
I shall return to it presently. 

The substitution of machines for human labor raises problems 
which are likely to become acute in the not very distant future. These 
problems are not new. They began with the Industrial Revolution, 
which ruined large numbers of skilled and industrious handicrafts- 
men, inflicting upon them hardships that they had in no way deserved 
and that they bitterly resented. But their troubles were transitory: they 
died; and such of their children as survived sought other occupations. 
The sufferers had no political power and were not able to offer any 
effective resistance to "progress." Nowadays, in democratic countries, 
the political situation is different and wage earners cannot be expected 
to submit tamely to starvation. But if we are to believe Norbert 
Wiener's book on cybernetics and I see no reason why we should 
not it should soon be possible to keep up the existing level of pro- 
duction with a very much smaller number of workers. The more eco- 
nomical methods, one may suppose, would be introduced during a 
war while the workers were at the front, if such a war were not quickly 
ended by H-bomb extermination, and when the survivors returned 
their former jobs would no longer be available. The social discontent 
resulting from such a situation would be very grave. It could be dealt 
with in a totalitarian country, but a democracy could only deal with 
it by radical changes in its social philosophy and even in its ethics. 
Work has been thought to be a duty, but in such a situation there 
would be little work to do and duty would have to take new forms. 

Changes in political philosophy are necessary for several reasons. 
One of the most important is that modern techniques make society 
more organic in the sense that its parts are more interdependent and 
an injury to one individual or group is more likely than it formerly was 
to cause injury to other individuals or groups. It is easier to kill a man 
than to kill a sponge because he is more highly organized and more 
centralized. In like manner it is easier to inflict vital damage upon a 
scientific community than upon a community of nomads or scattered 



JO What Is Science? 

peasants. This increase of interdependence makes it necessary to limit 
freedom in various ways which liberals in the past considered unde- 
sirable. There are two spheres in which such limitation is especially 
necessary: the one is in economics; and the other, in the relations be- 
tween states. 

Take economics first. Suppose, as is not improbable, that most of 
the power used in industry comes to be distributed from a fairly small 
number of atomic power-stations, and suppose that the men working 
in these stations retained the right to strike. They could completely 
paralyze the industrial life of a nation and could levy almost unlimited 
blackmail in the form of demands for higher wages. No community 
would tolerate such a state of affairs. The workers in power-stations 
would have to have understudies like actors in a theater, and the 
forces of the state would have to be employed if necessary to enable 
the understudies to replace workers on strike. Another example, which 
war has already brought to the fore, is the supply and use of raw ma- 
terials. Whenever raw materials are scarce their distribution has to be 
controlled and not left to the free play of unfettered economic forces. 
Scarcity of this sort has hitherto been thought of as a transitory phe- 
nomenon due to the needs and ravages of war. But it is likely to re- 
main, in regard to many essentials, a normal condition of highly 
developed industry. Some central authority for the allocation of raw 
materials must therefore be expected as a necessary limitation of 
economic freedom. Another unavoidable limitation comes from the 
vastness of some obviously desirable enterprises. To bring fertility to 
the interior of Australia and to parts of Siberia is almost certainly pos- 
sible, but only by an expenditure far beyond the capacity of private 
enterprise. One may expect that the progress of science will increase 
the number of such possible enterprises. Perhaps it will be possible 
in time to make the Sahara rainy, or even to make northern Canada 
warm. But, if such things become possible, they will be possible only 
for whole communities and not for private corporations. 

Even more important than the limitations of economic liberty are 
the limitations on the liberty of states. The liberal doctrine of national- 
ity, which was preached by liberals before 1848 and embodied in the 
Treaty of Versailles by President Wilson, had its justification as a 
protest against alien domination. But to allow complete liberty to any 



Science and Human Life 11 

national state is just as anarchic as it would be to allow complete 
liberty to an individual. There are things which an individual must 
not do because the criminal law forbids them. The law and the police 
are in most cases strong enough to prevent such things from being 
clone: murderers are a very small percentage of the population of any 
civilized country. But the relations between states are not governed 
by law and cannot be until there is a supranational armed force strong 
enough to enforce the decisions of a supranational authority. In the 
past, although the wars resulting from international anarchy caused 
much suffering and destruction, mankind was able to survive them, 
and, on the whole, the risks of war were thought less irksome than the 
controls that would be necessary to prevent it. This is ceasing to be 
true. The risks of war have become so great that the continued exist- 
ence of our species either has become or soon will become incom- 
patible with the new methods of scientific destruction. 

The new dangers resulting from our more organic society call for 
certain changes in the kind of character that is admired. The bold 
buccaneer, or the great conqueror such as Alexander or Napoleon, 
has been admired and is still admired although the world can no 
longer afford this type of character. We come here upon a difficulty. 
It is a good thing that people should be adventurous and that there 
should be scope for individual enterprise; but the adventure and en- 
terprise, if they are not to bring total disaster, must steer clear of cer- 
tain fields in which they were formerly possible. You may still, with- 
out harm to your fellow men, wish to be the first man to reach the 
moon. You may wish to be a great poet or a great composer or a 
man who advances the boundaries of scientific knowledge. Such ad- 
venture injures no one. But if Napoleon is your ideal, you must be 
restrained. Certain kinds of anarchic self-assertion, which are splen- 
did in the literature of tragedy, have come to involve too much risk. 
A motorist alone on an empty road may drive as he pleases, but in 
crowded traffic he must obey the rules. More and more the lives of 
individuals come to resemble the motorist in traffic rather than the 
lonely driver in an empty desert. 

I come at last to a question which is causing considerable concern 
and perplexity to many men of science, namely: what is their social 
duty toward this new world that they have been creating? I do not 



12 What Is Science? 

think this question is easy or simple. The pure man of science, as 
such, is concerned with the advancement of knowledge, and in his 
professional moments he takes it for granted that the advancement of 
knowledge is desirable. But inevitably he finds himself casting his 
pearls before swine. Men who do not understand his scientific work 
can utilize the knowledge that he provides. The new techniques to 
which it gives rise often have totally unexpected effects. The men 
who decide what use shall be made of the new techniques are not 
necessarily possessed of any exceptional degree of wisdom. They are 
mainly politicians whose professional skill consists in knowing how to 
play upon the emotions of masses of men. The emotions which eas- 
ily sway masses are very seldom the best of which the individuals 
composing the masses are capable. And so the scientist finds that he 
has unintentionally placed new powers in the hands of reckless men. 
He may easily come to doubt, in moments of depression or overwork, 
whether the world would not be a happier place if science did not 
exist. He knows that science gives power and that the power which it 
gives could be used to increase human welfare; but he knows also 
that very often it is used, not so, but in the very opposite direction. 
Is he on this account to view himself as an unintentional malefactor? 
I do not think so. I think we must retain the belief that scientific 
knowledge is one of the glories of man. I will not maintain that 
knowledge can never do harm. I think such general propositions can 
almost always be refuted by well-chosen examples. What I will main- 
tain and maintain vigorously is that knowledge is very much more 
often useful than harmful and that fear of knowledge is very much 
more often harmful than useful. Suppose you are a scientific pioneer 
and you make some discovery of great scientific importance, and sup- 
pose you say to yourself, "I am afraid this discovery will do harm": 
you know that other people are likely to make the same discovery if 
they are allowed suitable opportunities for research; you must there- 
fore, if you do not wish the discovery to become public, either dis- 
courage your sort of research or control publication by a board of 
censors. Nine times out of ten, the board of censors will object to 
knowledge that is in fact useful e.g., knowledge concerning con- 
traceptives rather than to knowledge that would in fact be harmful. 
It is very difficult to foresee the social effects of new knowledge, and 



Science and Human Life 13 

it is very easy from the sheer force of habit to shrink from new 
knowledge such as might promote new kinds of behavior. 

Apart from the more general duties of scientists toward society, 
they have a quite special and exceptional duty in the present critical 
condition of the world. All men of science who have studied thermo- 
nuclear warfare are aware of two superlatively important facts: first, 
that whatever agreements may have been reached to the contrary, 
thermonuclear weapons will certainly be employed by both sides in a 
world war; second, that if such weapons are employed there can be 
no hope of victory for either side, but only of universal destruction 
involving, quite possibly, the end of all human and animal life and 
almost certainly, failing that, a complete reversion to barbarism. A 
great war with thermonuclear weapons will not produce a universal 
victory of communism. It will also not produce the sort of world de- 
sired by the Western Powers. Nor will it give opportunity for the 
independent flourishing of Southeast Asia or Africa. Radioactive 
clouds, borne by the wind, will not respect frontiers and will ignore 
the legal rights of neutrals. In view of this prospect, there is one mat- 
ter upon which the interests of the whole world coincide. Whether 
you are a Communist or an anti-Communist, an inhabitant of Asia 
or Europe or America, a white, brown, yellow or black man, your in- 
terests are exactly the same as those of the rest of the human race. 
Your paramount interest, if you are aware of the situation, must be 
to preserve the existence of mankind by preventing a great war. It is 
clearly the duty of men of science to bring the facts home, as far as 
lies in their power, to the governments and peoples of both East 
and West. This is no easy task. The governments of both East and 
West, whether from ignorance or from motives of prestige, are en- 
gaged in trying to persuade their populations that thermonuclear 
weapons will destroy the enemy but not themselves. The Red Star, 
the official military organ of the Soviet government, published sev- 
eral articles on methods of defense against thermonuclear weapons. 
These articles were so absurd that one could hardly believe their au- 
thors to be sincere. It seemed obvious that the purpose of the articles 
was to deceive people in Russia as to the perils to which they would 
be exposed. I am afraid that the schemes for civil defense put for- 
ward in America and Britain are equally misleading. I hope that this 



14 What Is Science? 

is because the authorities are ignorant and not because they are dis- 
honest. 

Clearly, scientists both of the East and of the West have an im- 
perative duty: namely, the duty of bringing home to the protagonists 
the fact that the time is past for swashbuckling and boasting and 
campaigns of bluff which, if the bluff is called, can end only in utter 
disaster. I have been glad to see a lead given by a small number of 
men of science of the highest eminence, representing many countries 
and all creeds, Americans, Western Europeans, Poles and Japanese. 
I have rejoiced to see these men issue a clear statement as to what is 
likely to happen in a great war; and I should wish them to invite all 
other men of science, in all countries, to subscribe to this statement. 

I am aware that this will involve a certain degree of heroism and 
self-sacrifice. But there will be a reward which brave men should find 
sufficient: the reward of preserving uprightness and self-respect in the 
face of danger. These virtues are common in battle, and men of sci- 
ence should be able to show them also in a conflict with ignorance 
and ferocity. Science has fought great fights in former centuries 
against the embattled forces of obscurantism. In the nineteenth cen- 
tury it seemed as though science were victorious, but the victory is in 
danger of proving illusory. If science is to do its duty by mankind, 
men of science must once again face martyrdom and obloquy and the 
accusation of indifference to moral values. Perhaps their prestige may 
suffice to save them from the worst penalties for their courage, but of 
this we cannot be confident. What we can say with confidence is 
that it is not worth while to prolong a slavish and cowardly existence 
for a few miserable years while those who know the magnitude of the 
impending catastrophe wait for that radioactive death that is in store 
for them as well as for others. 

A difficult readjustment in the scientists' conception of duty is im- 
peratively necessary. As Lord Adrian said in his address to the British 
Association, "Unless we are ready to give up some of our old loyal- 
ties, we may be forced into a fight which might end the human 
race." This matter of loyalty is the crux. Hitherto, in the East and in 
the West alike, most scientists, like most other people, have felt that 
loyalty to their own state is paramount. They have no longer a right 
to feel this. Loyalty to the human race must take its place. Everyone 



Science and Human Life 15 

in the West will at once admit this as regards Soviet scientists. We 
are shocked that Kapitza, who was Rutherford's favorite pupil, was 
willing, when the Soviet government refused him permission to return 
to Cambridge, to place his scientific skill at the disposal of those who 
wished to spread communism by means of H-bombs. We do not so 
readily apprehend a similar failure of duty on our own side. I do not 
wish to be thought to suggest treachery, since that is only a transfer- 
ence of loyalty to another national state; I am suggesting a very dif- 
ferent thing: that scientists the world over should join in enlighten- 
ing mankind as to the perils of a great war and in devising methods 
for its prevention. I urge with all the emphasis at my disposal that 
this is the duty of scientists in East and West alike. It is a difficult 
duty, and one likely to entail penalties for those who perform it. 
But, after all, it is the labors of scientists which have caused the dan- 
ger and on this account, if on no other, scientists must do everything 
in their power to save mankind from the madness which they have 
made possible. 

Science from the dawn of history, and probably longer, has been 
intimately associated with war. I imagine that when our ancestors de- 
scended from the trees they were victorious over the arboreal con- 
servatives because flints were sharper than coconuts. To come to 
more recent times, Archimedes was respected for his scientific defense 
of Syracuse against the Romans; Leonardo obtained employment un- 
der the Duke of Milan because of his skill in fortification, though he 
did mention in a postscript that he could also paint a bit; Galileo 
similarly derived an income from the Grand Duke of Tuscany be- 
cause of his skill in calculating the trajectories of projectiles. In the 
French Revolution, those scientists who were not guillotined devoted 
themselves to making new explosives. There is therefore no depar- 
ture from tradition in the present-day scientists' manufacture of 
A-bombs and H-bombs. All that is new is the extent of their destruc- 
tive skill. 

I do not think that men of science can cease to regard the disin- 
terested pursuit of knowledge as their primary duty. It is true that 
new knowledge and new skills are sometimes harmful in their effects, 
but scientists cannot profitably take account of this fact since the ef- 
fects are impossible to foresee. We cannot blame Columbus because 



16 What Is Science? 

the discovery of the Western Hemisphere spread throughout the East- 
ern Hemisphere an appallingly devastating plague. Nor can we blame 
James Watt for the Dust Bowl, although if there had been no steam 
engines and no railways the West would not have been so carelessly 
or so quickly cultivated. To see that knowledge is wisely used is pri- 
marily the duty of statesmen, not of men of science; but it is part of 
the duty of men of science to see that important knowledge is widely 
disseminated and is not falsified in the interests of this or that propa- 
ganda. 

Scientific knowledge has its dangers; but so has every great thing. 
And over and beyond the dangers with which it threatens the pres- 
ent, it opens up as nothing else can the vision of a possible happy 
world, a world without poverty, without war, with little illness. And, 
what is perhaps more than all, when science has mastered the forces 
which mold human character, it will be able to produce populations 
in which few suffer from destructive fierceness and in which the great 
majority regard other people, not as competitors to be feared, but as 
helpers in a common task. Science has only recently begun to apply 
itself to human beings, except in their purely physical aspect. Such 
science as exists in psychology and anthropology has hardly begun to 
affect political behavior or private ethics. The minds of men remain 
attuned to a world that is fast disappearing. The changes in our phys- 
ical environment require, if they are to bring well-being, correlative 
changes in our beliefs and habits. If we cannot effect these changes, 
we shall suffer the fate of the dinosaurs who could not live on dry 
land. I think it is the duty of science I do not say of every indi- 
vidual man of science to study the means by which we can adapt 
ourselves to the new world. There are certain things that the world 
quite obviously needs: tentativeness, as opposed to dogmatism, in 
our beliefs; an expectation of co-operation, rather than competition, 
in social relations; a lessening of envy and collective hatred. These 
are things which education could produce without much difficulty. 
They are not things adequately sought in the education of the pres- 
ent day. 

It is to progress in the human sciences that we must look to undo 
the evils which have resulted from a knowledge of the physical world 
hastily and superficially acquired by populations unconscious of the 



Science and Human Life 17 

changes in themselves that the new knowledge has made imperative. 
The road to a happier world than any known in the past lies open 
before us if atavistic destructive passions can be kept in leash while 
the necessary adaptations are made. Fears are inevitable in our time, 
but hopes are equally rational and far more likely to bear good fruit. 
We must learn to think rather less of the dangers to be avoided than 
of the good that will lie within our grasp if we can believe in it and 
let it dominate our thoughts. Science, whatever unpleasant conse- 
quences it may have by the way, is in its very nature a liberator, a 
liberator of bondage to physical nature and, in time to come, a lib- 
erator from the weight of destructive passions. We are on the thresh- 
old of utter disaster or unprecedentedly glorious achievement. No 
previous age has been fraught with problems so momentous; and it is 
to science that we must look for a happy issue. 



MATHEMATICS AND 
LOGIC 

SIR EDMUND TAYLOR WHITTAKER 



about 

Sir Edmund Taylor Whittaker 



Sir Edmund Whittaker, one of the world's foremost mathematicians, 
has had a distinguished professional career reaching back into the 
last century. Few men still living have known intimately and worked 
together with so many of those who made the revolution of modern 
science. The following autobiographical sketch contains historical 
side lights which will, I believe, delight the reader and give him in- 
formation not otherwise obtainable. 

"I was born at Southport, England, on October 24, 1873, the son 
of John Whittaker and Selina, daughter of Edmund Taylor, M.D. At 
the age of eleven I was sent away from home to the Manchester 
Grammar School. I was on the classical side, which meant that three- 
fifths of my time was devoted to Latin and Greek. In the lower forms, 
where the study was purely linguistic, I did well, but my lack of 
interest in poetry and drama caused a falling-off when I was pro- 
moted to the upper school, and I was glad to escape by electing to 
specialize in mathematics. Only after I had left school did I discover 
the field of Latin and Greek learning that really appealed to me 
ancient and medieval theology, philosophy and science. 

"I gained an entrance scholarship to Trinity College, Cambridge 
in 1891, and was elected a Fellow of Trinity in 1896 and put on the 
lecturing staff. Among my pupils at Trinity in 1896-1906 were the 
well-known mathematicians G. H. Hardy, Sir fames Jeans, Harry 

20 



about Sir Edmund Taylor Whittaker 21 

Bateman, Sir Arthur Eddington, J. E. Littlewood, G. N. Watson, 
H. W. Turnbull, and Sir Geoffrey Taylor. 

"The professor of pure mathematics at this time v^as A. R. 
Forsyth, a sociable and hospitable man who liked entertaining 
mathematicians from the continent of Europe. I lived in the next 
rooms to him in college and was always invited to meet them: and 
in this way I came to know Felix Klein, who was a frequent visitor 
and for whom I had a great admiration and affection, and also Henri 
Poincart and G. Mittag-Leffler. 

"In 1898, 1899 and 1900 I acted as one of the secretaries of the 
mathematical and physical section of the British Association for the 
Advancement of Science. This was a valuable experience for such a 
young man, for I was brought into close contact with the great math- 
ematical and experimental physicists of the older generation Lord 
Kelvin, Lord Rayleigh, Sir George Stokes and G. F. FitzGerald; and 
those of the generation still in its prime Sir /. /. Thomson, Sir 
Joseph Larmor, Sir Arthur Schuster and Sir Oliver Lodge; and my 
own contemporaries, such as Lord Rutherford. 

"I became a Fellow of the Royal Astonomical Society in 1898 
and was appointed one of its secretaries in 1901. Here again I was 
brought into contact with many senior men of great distinction, par- 
ticularly Sir William Huggins, who first applied spectroscopy to the 
stars, and Sir Norman Lockyer, and with others who though not 
famous astronomers were celebrated in other ways notably Admiral 
Sir Erasmus Ommaney, who was a very old man when I knew him 
but attended the meetings regularly; he had fought (I presume as a 
midshipman) at the battle of Navarino in 1827, when the Turkish 
fleet was destroyed by an allied fleet under Codrington, and Greece 
was liberated. 

"I left Trinity in 1906 on being appointed Royal Astronomer of 
Ireland the office held in 1827-1865 by Sir William Rowan Hamil- 
ton, the discoverer of quaternions and 4)f Hamiltonian methods in 
optics and dynamics. My most distinguished pupil in Dublin was 
Eamon de Valera, who has never ceased to follow mathematics as a 
recreation from his political activities. About the end of my time in 
Ireland he was a candidate for a vacant chair of mathematics in 
Galway: I was asked my opinion and said that he was a man who 



22 What Is Science? 

would go far a prediction fulfilled in a way I did not at the time 
anticipate. 

"In 1912 I 'was elected to the historic chair of mathematics in the 
University of Edinburgh, which had been occupied in 1674-1675 by 
Gregory and in 1725-1746 by Maclaurin. The epitaph composed 
for Maclaurin by Johnson when he and Boswell visited Scotland is 
still to be read in Greyfriars Kirkyard, and tells how Maclaurin was 
elected to the chair electus ipso Newtono suadente. 

"In Edinburgh from 1912 to 1946 I had many undergraduate and 
postgraduate pupils who afterwards rose to distinction; two boys who 
came up from school together one year, and later became Fellows of 
the Royal Society, were W. V. D. Hodge, who now holds the 
Lowndean chair of Geometry at Cambridge, and my son J. M. W/iit- 
taker, now vice-chancellor of the University of Sheffield. I gave many 
lectures or courses of lectures at other universities which were after- 
wards printed: The Rouse Ball and Tamer lectures at Cambridge, 
the Herbert Spencer lectureship at Oxford, the Donnellan lecture- 
ship in Dublin, the Riddell lectureship at Durham (Newcastle), the 
Selby lectureship at Cardiff, the Hitchcock professorship at the Uni- 
versity of California, the Bruce-Preller lectureship at the Royal 
Society of Edinburgh, the Larmor lectureship at the Royal Irish 
Academy, and the Guthrie lectureship of the Physical Society. 

"In connection with the Edinburgh chair, I may mention the in- 
stitution in 1914 of what was, so far as I know, the first university 
mathematical laboratory, which incorporated in mathematical teach- 
ing the theory of computation as known to professional astronomers. 

"From other universities I received the honorary degrees of LL. D. 
(St. Andrews and California) and Sc. D. (Dublin, National Uni- 
versity of Ireland, Manchester, Birmingham and London). 

"I was elected F.R.S. in 1905, served on the Council and was 
awarded the Sylvester and Copley medals. With the Royal Society of 
Edinburgh I had continuous contact, being president in 1939-1944. 
At the end of my tenure of the presidency, a bronze portrait head, 
executed by Mr. Benno Schotz, R.S.A., was subscribed for by the 
Fellows and placed in the Society's house. I was president of the 
Mathematical Association in 1920-21, of the Mathematical and 
Physical Section of the British Association in 1927, and of the Lon- 



about Sir Edmund Taylor Whittaker 23 

don Mathematical Society in 1928-1929, being awarded its De 
Morgan Medal in 1935. 

"I am an Honorary Fellow or Foreign Member of many national 
academies or mathematical societies and of my old college, Trinity, 
and H. H. Pope Pius XI appointed me a member of the pontifical 
Academy of Sciences and conferred on me the Cross pro Ecclesia et 
Pontifice." 

Sir Edmund's many writings include Modern Analysis (in collab- 
oration with G. N. Watson), Treatise on Analytical Dynamics, The- 
ory of Optical Instruments, History of the Theories of Aether and 
Electricity, The Calculus of Observations, The Beginning and End 
of the World, and his Tamer Lectures, From Euclid to Eddington. 
He is held in as high regard for his works on the philosophy and 
history of science as for those on purely mathematical subjects. 

Whittaker was knighted in 1945. Now in his 82nd year he con- 
tinues with remarkable vigor to pursue his writings and researches. 
The second volume of his History of the Theories of Aether and 
Electricity, a monumental history of the whole of theoretical physics 
was published in 1953. He is at work on the third volume which will 
take the story up to 1950. The following essay is a tour de force, 
surveying modern mathematics and logic, showing how they evolved 
from the mathematical interests of the past and describing some of 
the main problems mathematicians are working on today. I know of 
no one else who could have covered this vast field in such brief space, 
much less have made the discussion accessible in large part to the 
ordinary intelligent reader. 



MATHEMATICS AND LOGIC 

SIR EDMUND TAYLOR WHITTAKER 



The First Mathematicians 

Mathematics is in this book regarded as a kind of science. But there 
is a great difference between mathematics and the other recognized 
branches of science, as can be seen when we examine the nature of a 
typical mathematical theorem. Take for instance this, which was orig- 
inally enunciated in the eighteenth century by Edward Waring of 
Cambridge: "Every positive whole number can be represented as the 
sum of at most nine cubes." With Waring this was really no more 
than a guess based on observation of a great number of particular 
cases; but evidently mere observation cannot furnish a proof that the 
theorem is true in general, and indeed a strict proof of this theorem 
was not known until more than a century later. Let us see how the 
notion of a science that depends on logical proof came into being. 

Historians are generally agreed that this development originated 
with the Greek philosophers of the sixth and fifth centuries before 
Christ. To be sure, the arts of calculation and measurement had 
made considerable progress before this, amongst the ancient Baby- 
lonians and Egyptians, who were able to solve numerical problems 
beyond the powers of most modern schoolboys; but the procedure 
which is characteristic of mathematics as we know it, the proving of 
theorems, was introduced by the Greeks. 

The records are scanty, and generally later in date by some centu- 

24 



Mathematics and Logic 25 

ries than the events referred to. But there can be no doubt that the 
movement began in the fringe cf Greek settlements along the coast 
of Asia Minor, which were in contact with the older civilizations of 
the East, and were at the time enjoying peace and prosperity. The 
new principle that was central in their philosophy was the conviction 
that the world has a unity; in a polytheistic society they were essen- 
tially monotheists, and they held that science is of one pattern. The 
first of them whose name has come down to us, Thales of Miletus 
(6407-546 B.C.) taught that all matter is essentially one, that it con- 
sists, in fact, of modifications of water. His successor, Anaximander, 
the second head of the school, opened wider possibilities by asserting 
only that there is one primitive formless substance everywhere pres- 
ent, out of which all things were made. 

Thales is credited with the discovery of the mathematical theorem 
that "the angle in a semicircle is a right angle." This differs in char- 
acter from the geometrical facts known to the ancient Egyptians, 
which had been concerned with areas. Thales seems to have been the 
first thinker to make lines and curves (which are abstractions) funda- 
mental. For him, the theorem was probably a simple fact of observa- 
tion. He would be familiar with wall decorations in which rectangles 
were inscribed in circles: a diagonal of a rectangle is also a diagonal 
of the corresponding circle, and the right angle formed by two sides 
of the rectangle is therefore the angle standing on a diameter, i.e., 
it is the angle in a semicircle. 



The Place of Logic in Geometry 

The disciples of Thales based their doctrine of physics on the assump- 
tion of a single ever-present medium which could undergo modifica- 
tions. So far as the relations of physical objects with each other were 
concerned, they knew little beyond the experimental arts of survey- 
ing and measuring which they had inherited from the Egyptians and 
Babylonians. The Greeks of the next generation, however, developed 
this primitive geometry into an independent science, in which the 
whole corpus of the properties of figures in space, such as the theo- 
rem that the angle in a semicircle is a right angle, were deduced 



26 



What Is Science? 



logically from a limited number of principles which were regarded as 
obviously true and so could be assumed: such as that if equals are 
added to equals, the sums are equal and the -whole is greater than its 
parts. These principles were given the name of common notions 
(koinai ennoiai), and later of axioms (axiomata). 

This rational geometry was discovered not by the philosophers of 
Asia Minor (who disappear from history no't long afrcr rhe fall of 
Miletus in 494 B.C., but by another school which sprang up in the 
Greek settlements in southern Italy, and which took the name of 
Pythagoreans from its founder Pythagoras (582?-aft. 507 B.C.). The 
famous theorem, that in a right-angled triangle the sum of the squares 
of the sides containing the right angle is equal to the square of the 
hypotenuse, is called by his name, probably with justice, though the 
Babylonians had methods of finding the length of the hypotenuse 
which doubtfully suggest some knowledge of it. It may seem strange 
that a proposition whose proof (as given in modern textbooks) is 
comparatively difficult, should have become known at such an early 
stage in the history of the subject; but it must be explained that the 
Pythagoreans had inherited from the pyramid-builders of Egypt the 
notion of similarity in figures, and that Pythagoras' theorem can be 
proved very easily when this notion is used. Thus, if ACB is a trian- 
gle right-angled at C, and CK is perpendicular to AB, then the tri- 
angle ACB is the sum of the triangles ACK and CKB. But these are 
three similar triangles, and their areas are proportional to the areas of 
any other figures erected on the corresponding sides, which are sim- 
ilar to each other, in particular to the squares on these sides: whence 
immediately we have AC 2 + CB 2 = AB 2 . 



Mathematics and Logic 27 

The new field of rational geometry was recognized as one in which 
progress was possible indefinitely; and practically the whole of the 
geometry now studied in schools was discovered by the Pythagoreans 
between 550 B.C. and 400 B.C. 

To Thales' principle, that different kinds of matter are portions of 
a primitive universal matter, Pythagoras adjoined another principle, 
namely that the differences between different kinds of matter ate due 
to differences in geometrical structure, or form. Thus the smallest 
constituent elements of fire, earth, air, and water, were respectively 
a tetrahedron, a cube, an octahedron, and an icosahedron. This be- 
lief led to much investigation on the theory of the regular solid bod- 
ies, which is the underlying subject of the great work in which the 
Pythagorean geometry was eventually set forth, the Elements of Eu- 
clid.* 



The Discovery of Irrationals 

The Pythagoreans held that the principles of unity, in terms of which 
the cosmos was explicable, were ultimately expressible by means of 
numbers; and they attempted to treat geometry numerically, by re- 
garding a geometrical point as analogous to the unit of number 
a unit which has position^ as they put it. A point differs from the unit 
of number only in the additional characteristic that it has location; 
a line twice as long as another line was supposed to be formed of 
twice as manv points. Thus space was regarded as composed of sep- 
arate indivisible points, and time of separate instants; for when the 
Greeks spoke of number, they always meant whole number. A pros- 
pect was now opened up of understanding all nature under the as- 
pect of countable quantity. This view was confirmed by a striking 
discovery made by Pythagoras himself, namely that if a musical note 
is produced by the vibration of a stretched string, then by halving 
the length of the string we obtain a note which is an octave above 

* For the important contributions made by the Babylonians to algebra and geom- 
etry the reader is referred to an admirable survey of ancient mathematics incorpo- 
rating the researches of the past 25 years, especially on cuneiform tablets: B. L. 
Van der Waerden, Science Awakening, Groningen (Holland), 1955. Ed. 



28 What Is Science? 

the first note, and by reducing the length to two-thirds of its original 
value we obtain a note which is at an interval of a fifth above it. 
Thus structure, expressible by numerical relations, came to be re- 
garded as the fundamental principle of the universe. 

In carrying out the program based on this idea, however, the Py- 
thagoreans came upon difficulties. For instance, they asked, what is 
the ratio of the number of points in the side of a square to the num- 
ber of points in the diagonal? Let this ratio be m : n where m and n 
are whole numbers having no common factor. Then since the square 
of the diagonal is, by Pythagoras' theorem, twice the square of the 
side, we have n 2 = 2m 2 . From this equation it follows that n is an 
even number, say n 2/>, where p is a whole number. Therefore 
m 2 = 2p 2 , so m also is even, and therefore m and n have a common 
factor, contrary to hypothesis. Hence the ratio of the number of 
points in the side of a square to the number of points in the diago- 
nal cannot be expressed as a ratio of whole numbers: we have made 
the discovery of irrational numbers. Since ratios such as this could 
exist in geometry but could not exist in the arithmetic of whole num- 
bers, the Pythagoreans concluded that continuous magnitude cannot 
be composed of units of the same character as itself, or in other 
words, that geometry is a more general science than arithmetic. 



The Paradoxes of Zeno 

The logical difficulty created by the discovery of irrationals was soon 
supplemented by others, which the Greek philosophers of the fifth 
century B.C. constructed in their attempts to understand some of the 
fundamental notions of mathematics. 

Let a ball be bouncing on a floor, and suppose that whenever it 
hits the floor it bounces back again, and remains in the air for half 
as long a time as on the preceding bounce. Will it ever stop bounc- 
ing? 

If the duration of the first bounce is taken as 1, then the durations 
of the succeeding bounces are }/2, ! /4, Vs, etc., and the sum of these 
durations is 1 -f Yi + 1 A -f- Ys + . Now let these durations be 
represented on a line: if C is the middle point of a line AB and if D 



Mathematics and Logic 29 

is the middle point of CB, E the middle point of DB, F the middle 
point of EB, and so on, then if AC = 1, 



A C D E F B 

we have CD = Vi, DE = V*, EF = V&, etc., and the whole length 
AB is 

1 + i/ 2 + y 4 + i/ 8 + . . . . 

But the whole length is 2. So after a time 2, the bouncing mil have 
stopped, a fact which is perhaps at first sight difficult to understand 
when we reflect that whenever the ball comes down, it goes up again. 
A famous paradox, due to Zeno (4907-435 B.C.) is that of the 
race between Achilles and the tortoise. The tortoise runs (say) one- 
tenth as fast as Achilles, but has a start of (say) 100 yards. By the 
time Achilles has run this 100 yards and is at the place the tortoise 
started from, the tortoise is 10 yards ahead: when Achilles has cov- 
ered this 10 yards, the tortoise is 1 yard ahead: and so on forever 
Achilles never catches up. This conclusion is obviously contrary to 
common sense. But we may remark that if Achilles is required to ring 
a bell every time he reaches the spot last occupied by the tortoise, 
then there will be an infinite number of such occasions, and the 
time required for the overtaking will indeed be infinite. The point is, 
that a finite stretch of space can be divided into an infinite number 
of intervals, and if those intervals are noted in review one by one, 
then the time required for the review is infinite. 

The Beginnings of Solid Geometry in the Atomistic School 

About the end of the fifth century B.C., some philosophers, of whom 
the most celebrated was a Thracian named Democritus, accepted the 
existence of empty space (which had been denied by the school to 
which Zeno belonged) and taught that the physical world is com- 
posed of an infinite number of small hard indivisible bodies (the 
atoms) which move in the void. All sensible bodies are composed of 
groupings of atoms. This notion was applied in order to calculate the 
volume of a cone or pyramid. The pyramid was conceived as a pile 



30 



What Is Science? 



of shot, arranged in layers parallel to the base, the quantity of shot 
in any layer being proportional to the area of the layer and so to the 
square of the distance of the layer from the vertex of the pyramid. 
Then by summing the layers, it was found that the volume of the 
cone or pyramid is one-third the volume of a prism of the same height 
and base. 

The Parallel Axiom 

When the Greek philosophers based mathematics on axioms, they be- 
lieved axioms to be true statements, whose truth was so obvious that 
they could be accepted without proof. One of the axioms they used, 
however, was felt to be not perfectly obvious, and for over twenty 
centuries attempts were made to prove it, by deducing it from other 
axioms which could be more readily admitted. This parallel axiom, as 
it is called, was stated by Euclid thus: if a straight line falling on two 
straight lines makes the interior angles on the same side less than two 
right angles, the two straight lines, if produced indefinitely, meet on 
that side on which are the angles less than two right angles. 

Euclid himself seems to have had some hesitation about it, for he 
avoided using it in his first 28 propositions. He wished, however, to 
study parallel lines (that is, lines which are in the same plane, and, 
being produced ever so far both ways, do not meet), and he found 
that a theory of parallel lines could not be constructed without this 
axiom or something equivalent to it. 

The Greeks, although they did not really doubt the truth of the 
parallel axiom, constructed arguments which seemed to disprove it. 
Thus, let AB be a straight line falling on two straight lines AK, BL, 
and making the interior angles on the same side KAB, LBA, to- 
gether less than two right angles. On AK take AC = 1/2 AB and 
on BL take BD = 1/2 AB. Then the lines AK, BL, cannot meet 



Mathematics and Logic 31 

within the ranges AC, BD, since if they did, two sides of a triangle 
would be less than the third side. We now have the line CD falling 
on the two straight lines CK, DL, and making the interior angles on 
the same side less than two right angles, so we can repeat the argu- 
ment. By repeating it indefinitely often, we can conclude that the 
two lines AK, BL, will never meet. The fallacy in the argument is of 
course the same as in the paradox of Achilles and the tortoise. 
Namely, the distance from A to the meeting-point is by this process 
divided into an infinite number of segments; if we consider the oper- 
ation of forming these segments one by one in turn, we shall never 
come to the end of the process. 

Many axioms have been proposed at different times as substitutes 
for the parallel axiom, capable of leading logically to the theory of 
parallels; one such axiom consists in affirming the existence of trian- 
gles similar to each other, but of different sizes; and another axiom 
consists in the statement that two straight lines which intersect one 
another cannot both be parallel to the same straight line. Either of 
these two substitutes seems to be more obviously true than Euclid's 
parallel axiom; but early in the eighteenth century an Italian Jesuit 
named Saccheri (1667-1733) thought of what seemed a still better 
plan, namely to prove Euclid's original parallel axiom by showing 
that a denial of its truth leads to a reductio ad absurdum. He carried 
out this program and showed that when the parallel axiom is not as- 
sumed, a logical system of geometry can be obtained, which however 
differs in many respects from the geometry universally believed to be 
true: for instance, the sum of the angles of a triangle is not equal to 
two right angles. Saccheri considered that by arriving at this result 
he had achieved his aim of obtaining a reductio ad absurdum and 
thereby had shown that the parallel axiom is true. He never for one 
moment imagined that the system he had found could be proposed 
as an alternative to Euclidean geometry for the description of actual 
space. 

The Geometry of Astronomical Space 

In the nineteenth century however, some doubts were expressed as to 
whether the properties of space were represented everywhere and at 



32 What Is Science? 

all times by the geometry of Euclid. "The geometer of to-day," wrote 
W. K. Clifford (1845-1879), "knows nothing about the nature of the 
actually existing space at an infinite distance: he knows nothing 
about the properties of the present space in a past or future eternity." 

Let us look into this question by considering a triangle in astro- 
nomical space, having its vertices, say, at the sun and two of the most 
distant nebulae, and having as its sides the paths of light-rays be- 
tween these vertices. Then at each of the three vertices there will be 
an angle between the two sides that meet there. Have we any rea- 
son to believe that the sum of these three angles at the vertices will 
be equal to two right angles? Obviously it is not practicable to sub- 
mit the matter to the test of observation; and we can find no logical 
reason for believing that the sum must necessarily be two right an- 
gles, since Saccheri's work showed that Euclidean geometry is not a 
logical necessity. Euclidean geometry is certainly valid, to a very close 
degree of approximation, for the triangles that we can observe in the 
limited space of a terrestrial laboratory. In their case its departure 
from truth is imperceptible, but for much larger triangles we must 
admit that neither logic nor observation gives us any decision. 

We must therefore regard it as possible that in the astronomical 
triangle the sum of the three angles may be different from two right 
angles. We must recognize that empty space may have properties af- 
fecting measurements of size, distance, and the like: in astronomical 
space the geometry is possibly not Euclidean. 

A language has been invented by mathematicians to describe this 
state of affairs. We know that the geometry of figures drawn on a 
curved surface, for instance the surface of a sphere, is different from 
the geometry of figures drawn in a plane, which is Euclidean; and 
this suggests a way of speaking about a three-dimensional space in 
which the geometry of solid bodies is not Euclidean: we say that in 
such a case, the space is curved. Astronomical space, then, may have 
a small curvature. This has long been recognized as a possibility, but 
it was not until the present century that the idea was developed into 
a definite quantitative theory. In 1929 the American astronomer 
E. P. Hubble announced as an observational fact that the spectral 
lines of the most distant nebulae are displaced toward the red end 



Mathematics and Logic 33 

of the spectrum, by amounts which are proportional to the distance 
of the nebulae. This red-displacement was interpreted to mean that 
the nebulae were receding from us with velocities proportional to 
their distances; in fact, that the whole universe was expanding, all 
distances continually increasing proportionally to their magnitudes. 
Combining this with the results of theoretical investigation, Edding- 
ton in 1930 published a mathematical theory of the nature of space, 
in which he supposed that astronomical space is not Euclidean, and 
that the deviation from Euclidean character depends not only on the 
size of the geometrical configuration considered, but also on the time 
that has elapsed since the creation of the world. This, which is 
known as the theory of the expanding universe, was generally ac- 
cepted and developed for the next 23 years. Values were found for 
the total mass, extent, and curvature of the universe; but in 1953 a 
new explanation of the red-displacement was proposed by E. Finlay- 
Freundlich, and the question is still under discussion. 



General Relativity 

The deviations from Euclidean properties which have just been con- 
sidered have a uniform character over vast regions of space. Accord- 
ing to the theory of General Relativity, there are also deviations 
which vary considerably within quite small distances, and which are 
due to the presence of ordinary gravitating matter. Something of the 
kind was conjectured by the Irish mathematical physicist G. F. Fitz- 
gerald when toward the end of the nineteenth century he said, 
"Gravity is probably due to a change of structure in the ether, pro- 
duced by the presence of matter." Perhaps he thought of the change 
of structure as being something like change in specific inductive ca- 
pacity or permeability. However, Einstein in 1915 published a defi- 
nite mathematical theory, in which gravitational effects were attrib- 
uted to a change in the curvature of the world, due to the presence of 
matter; and he showed that by this hypothesis it was possible to ac- 
count for a peculiarity of the orbit of the planet Mercury which was 
not explained by the older Newtonian theory. 



34 What Is Science? 

The Non-Euclidean Geometries 

We shall now describe some of the features of the non-Euclidean 
geometries that are obtained by assuming the parallel axiom to be 
untrue for geometry in the plane. 

If we consider a straight line CD and a point P not on it, then 
either: 

( 1 ) it may be impossible to draw any straight line through P that 
does not intersect CD. The geometry is then said to be elliptic. 

(2) or it may be possible to draw an infinite number of straight 
lines through P that do not intersect CD. The geometry is then said 
to be hyperbolic. 

Between these possibilities there is an intermediate case, in which it 
is possible to draw one and only one line through P which does not 
intersect CD: this case corresponds to ordinary Euclidean geometry. 

In elliptic geometry the sum of the angles of a triangle is always 
greater than two right angles. Every straight line, when it attains a 
certain length, returns into itself like the equator on a sphere, so the 
lengths of all straight lines are finite, and the greatest possible dis- 
tance apart of two points is half this length. The perpendiculars to a 
straight line at all the points on it meet in a point. 

In hyperbolic geometry, the sum of the three angles of a triangle 
is always less than two right angles; and indeed, the greater the area 
of the triangle, the smaller is the sum of its angles. If we consider a 
straight line CD, and a point P outside it, then we can draw two 
straight lines through P, PA and PB, which are not in the same 
straight line, with the properties that ( 1 ) any line through P which 
lies entirely outside the angle APB does not intersect the line CD, 
(2) any line through P which is inside the angle APB intersects the 
line CD at a point at a finite distance from P, (3) the two lines 




Mathematics and Logic 35 

PA, PB, tend asymptotically at one end of the line CD at infinity, 
so we may say they intersect it at infinity and are more or less 
analogous to Euclidean parallels: they are, in fact, called parallels to 
the line CD drawn through the point P. Lines which are parallel to 
each other at any point are parallel along their whole length, but 
parallels are not equidistant: the distance between them tends to 
zero at one end and to infinity at the other. 

Topology 

The opinion that the material universe is formed of atoms, which 
are eternal and unchangeable, had been held by many of the ancient 
Greek philosophers and was generally accepted by European phys- 
icists in the nineteenth century. An attempt to account for it mathe- 
matically was made in 1887 by William Thomson (Lord Kelvin), 
who after seeing a display of smoke-rings in a friend's laboratory, 
pointed out that if the atoms of matter are constituted of vortex 
rings in a perfect fluid, then the conservation of matter can be im- 
mediately explained, and the mutual interaction of atoms can be 
illustrated. In 1876 P. G. Tait of Edinburgh, having the idea that 
different kinds of atoms might correspond to different kinds of 
knotted vortex rings, took up the study of knots as geometrical forms. 
This is a problem of a new kind, since we are not interested in the 
precise description of the curve of the cord, but only in the essential 
distinction between one kind of knot and another the reef-knot, the 
bowline, the clove hitch, the fisherman's bend, etc. The transforma- 
tions which change the curve of the cord but do not change the 
essential character of the knot were specially studied. Relations of 
this kind, i.e., relations which are described by such words as "external 
to," "right-handed," "linked with," "intersecting," "surrounding," 
"connected by a channel with," etc., are called topological, and the 
study of topological relations in general is called topology. 

Another topological problem which was studied in the early days 
of the subject arose in connection with the flow of an electric current 
through a linear network of conductors. The network is a set of 
points (vertices) connected together in pairs by conductors. We can 
inquire what is the greatest number of conductors that can be re- 



36 What Is Science? 

moved from the network in such a way as to leave all the vertices 
connected together in one linear series by the remaining conductors. 
The number as obtained is of importance in the general problem of 
flow through the network. 

The New Views of Axioms 

It has long been realized that the axioms stated by Euclid are in- 
sufficient as a basis for Euclidean geometry; he tacitly assumes many 
others which are not in his list. Among these may be mentioned 
axioms of association, such as "if two different points of a straight 
line are in a plane, then all the points of the straight line are in 
the plane"; axioms of order, such as "of three different points lying 
on a straight line, one and only one lies between the other two*'; 
and axioms of congruence, which assert the uniqueness of something 
that there is only one distinct geometrical figure with certain prop- 
erties: thus, a triangle is uniquely determined by two adjacent sides 
and the included angle. 

Questions arise also regarding the use made of diagrams in geo- 
metrical proofs. In an edition of Euclid the diagrams are accurately 
drawn, and their topological features, which may be seen by inspec- 
tion, are often essential to the proof. Thus let a diagram be drawn 
representing any triangle ABC with the line AE bisecting its angle 
A and the line DE perpendicular to its side BC at its middle point; 
if this is carelessly drawn, the point E of the intersection of AE and 
DE might be placed inside the triangle a topological error. But in 
that case, drawing perpendiculars EL to AB and EK to AC, we can 




Mathematics and Logic 37 

easily show that the triangles LEB and KEC are equal in all respects, 
and also the triangles EBD and ECD are equal in all respects, thus 
the angles ABC and ACB are equal, and the triangle ABC is isosce- 
les. Thus a wrong topological understanding has led to a proof that 
every triangle is isosceles. The axioms must therefore be such as to 
guard against any erroneous topological assumptions. A rigorously 
logical deduction of Euclidean geometry is a formidable affair. 

It is of course obvious that the theorems of geometry were dis- 
covered long before strict logical proofs were found for them. Archi- 
medes, the greatest of the Greek mathematicians, distinguishes be- 
tween investigating theorems (theorem) and proving them rigorously 
(apodeiknunai) . 

When it was realized that the parallel axiom is not universally and 
eternally true, opinion changed about the place of axioms in mathe- 
matics. It now came to be accepted that the business of the mathe- 
matician is to deduce the logical consequences of the axioms he as- 
sumes at the basis of his work, without regard to whether these axioms 
are true or not; their truth or falsehood is the concern of another 
type of man of science a physicist or a philosopher. Thus the hori- 
zon of the geometer was widened; instead of inquiring into the struc- 
ture of actual space, he studied various different types of geometry 
defined respectively by their axioms: Euclidean and non-Euclidean 
geometries and also geometries with a finite total number of points, 
and what are called non-Archimedean and non-Desarguesian geom- 
etries. A non-Archimedean geometry is one which denies the "axiom 
of Archimedes," namely that if two segments are given, there is al- 
ways a multiple of the smaller that exceeds the larger. A non- 
Desarguesian geometry is one in which the theorem of Desargues is 
not true, namely that if two triangles be such that the straight lines 
joining their vertices in pairs are concurrent, then the intersections 
of pairs of corresponding sides lie on a straight line. 

The Dangers of Intuition 

The recognition that an axiom is a statement which is assumed, 
without any necessary belief in its truth, brought a great relief to 
mathematicians; for intuition had led the older workers to believe in 



38 What Is Science? 

the truth of many particular assertions which were shown in the latter 
part of the nineteenth century to be false. The following is an ex- 
ample. We may for the present purpose define a continuous plane 
curve to be one in which, as we pass along the curve from a point 
P to a neighboring point Q, the length of the perpendicular from a 
point on the curve to any fixed straight line passes through all the 
values intermediate between the values that it has at P and Q. Now 
it is obvious that a continuous curve will, in general, have a tangent 
at every point. But this is not always the case, as can be shown by 
the following construction. Take a straight line of any length, divide 
it into three equal parts, and on the middle part as base erect an 
equilateral triangle. Delete the base of the triangle, so we are left 




with four segments of equal length forming a broken line. Divide 
each of these four segments into three equal parts, and as before 
erect an equilateral triangle on the middle part of each segment, and 
then delete the bases of these triangles, so now we have a broken 
line of 16 segments. Repeating this process indefinitely, we arrive in 
the limit at a broken line which is a definite curve, but has no tangent 
at any point. Examples of this kind made it impossible to accept the 
view generally held by Kantian philosophers, that mathematics is 
concerned with those conceptions which are obtained by direct in- 
tuition of space and time. 

The Plan of a Rigorous Geometry 

Euclid attempted to specify the subject matter of geometry by defi- 
nitions such as "a point is that which has no parts/' and "a straight 
line is a line which lies evenly with the points on itself/' Neither of 
these definitions is made use of in his subsequent work; and indeed. 



Mathematics and Logic 39 

the first is clearly worthless, since there exist many things besides 
points which have no parts, while the second is obscure. 

In a modern rigorous geometry, the point and the straight line are 
generally accepted as undefined notions, so that the pattern of a 
branch of mathematics is now: 

( 1 ) enumeration of the primitive concepts in terms of which all the 
other concepts are to be defined 

(2) definitions (i.e. short names for complexes of ideas) 

(3) axioms, or fundamental propositions which are assumed with- 
out proof. It is necessary to show that they are compatible with each 
other (i.e. by combining them we cannot arrive at a contradiction) 
and independent of each other (i.e. no one of them can be deduced 
from the others). The compatibility is often proved by translating 
the assumptions into the domain of numbers, when any inconsistency 
would appear in arithmetical form; and the independence may be 
proved (as the independence of the parallel axiom was proved) by 
leaving out each assumption in turn and showing that a consistent 
system can be obtained without it. 

(4) existence-theorems. The discovery of irrationals led the Py- 
thagoreans to see the necessity for these. Does there exist a five-sided 
polygon whose angles are all right angles? The Greek method of 
proving the existence of any particular geometrical entity was to give 
a construction for it; thus, before making use of the notion of the 
middle point of a line, Euclid proves, by constructing it, that a line 
possesses a middle point. The "problems" of Euclid's Elements are 
really existence-theorems. 

(5) deductions, which are the body and purpose of the work. 



Space Time 

Until the end of the nineteenth century it was believed that the 
universe was occupied by space, which had three dimensions, so that 
a point of it was specified by the length, breadth and height of its 
displacement from some point taken as origin. It was supposed that 
space was always the same, consisting of the same points in the same 
positions. Whoever might be observing it, two different observers, in 



40 What Is Science? 

motion relative to each other, would see precisely the same space. In 
order to specify the position of a particle at any time, it was necessary 
therefore to know only the three co-ordinates of the space-point at 
which it was situated, and the time. The way of measuring time was 
supposed to be the same for the whole universe. Events happening 
at different points of space were said to be simultaneous if the time 
co-ordinates of the two points were the same. 

This scheme collapsed in the early years of the present century, 
when the theory of relativity was discovered and it was shown that 
observers who are in motion relative to each other do not see the 
same space. If we consider a particular observer, moving in any way, 
then for him each particle in the universe will have three definite 
space co-ordinates and a definite time co-ordinate; but for a different 
observer, moving relatively to him, both the space co-ordinates and 
the time co-ordinates of the particle will in general be changed. When 
we label every point-event of space with its co-ordinates (x, y, z) as 
recognized by a particular observer, and also with its time t as rec- 
ognized by this observer, then all point-events are specified by the 
four co-ordinates (t, x, y, z), just as all points in ordinary space are 
specified by three co-ordinates (x, y, z). We speak of this fourfold 
aggregate of point-events as a four-dimensional manifold, which is 
tailed space time. If a value of t is specified, the points (t, x, y, z) 
which have this value of t form a three-dimensional manifold with 
coordinates (x, y, z), and this manifold represents a space formed 
of the points which are simultaneous for the observer whose time is 
t . The problem is to find a set of equations 

t' = t' (t,x,y,z): x' = x' (t,x,y,z): y' = Y (t,x,y,z): z' = z' (t,x,y,z) 

which rearranges the fourfold of point-events (t,x,y,z) so as to con- 
vert the spaces which are simultaneous for one observer into the 
spaces which are simultaneous for another observer. 

Numbers 

Although numbers have been in use since the earliest ages, it was not 
until the last quarter of the nineteenth century that any satisfactory 
philosophical explanation was given of what they are. 



Mathematics and Logic 41 

Number is a property not of physical objects in themselves, but of 
collections or classes of objects. We must begin by explaining what 
we mean by saying that two classes have the same ntimber. If we 
have a group of husbands and wives, and if we know that each 
husband has one wife and each wife has one husband, then we can 
affirm that the number of husbands is the same as the number of 
wives, even though we do not know what that number is. In other 
words, two classes between whose respective members a one-to-one 
correspondence can be set up, have the same number: to be precise, 
the same cardinal number, for a distinction is drawn between cardinal 
and ordinal numbers; ordinal numbers are defined only by reference 
to sets whose elements are arranged in serial order. This definition 
applies equally well whether the number is finite or not. Thus if 
two rays OAC, OBD, proceeding from a point O, cut off segments 
AB and CD from two straight lines, then we can set up a one-to-one 
correspondence between the points P of AB and the points Q of CD 
by radii OPQ, and we can say that AB has the same number of 
points as CD. 

We can, however, draw 
lines from another point 
Z to A and B; suppose 
that these lines cut the 
line CD in points E and 
F. Then the number of 
points in EF is the same 
as the number of points 
in AB, and therefore the 
same as the number of 
points in CD. 





42 What Is Science? 

We see therefore that in the case of infinite collections, the number 
of the whole is not necessarily greater than the number of the parts; 
and indeed, a transfinite number may be defined as the number of a 
collection which can be put into one-to-one correspondence with a 
part of itself: for example, the positive integers have a one-to-one 
correspondence with their squares; and, therefore, the number of the 
integers is equal to the number of their squares, although the squares 
form only a part of the whole collection of integers. 

The cardinal numbers can be arranged in order by use of the 
notions of greater and less, which can be thus defined: a cardinal 
m is greater than a cardinal n if there is a class which has m members 
and has a part which has n members, but there is no class which 
has n members and has a part which has m members. 

The addition and multiplication of two numbers can be readily 
defined. If A and B are two collections whose cardinal numbers are 
a and b, then a class C formed by combining the collections A 
and B has for cardinal number the sum a -f b. If we form a new 
collection, of which each element consists of one element taken 
from A, paired with one element taken from B, and if these pairs 
are taken in all possible ways, then the cardinal number of the new 
collection is the product ab. It is readily seen that sums and products 
so defined satisfy 

the associative law a (be) = (ab) c 
the commutative law ab = ba 
and the distributive law a (b + c) = ab + ac 



Transfinite Numbers 

Until seventy years ago, infinity was a somewhat vague, general con- 
cept, and mathematicians did not know that transfinite numbers of 
different magnitudes could be accurately defined and distinguished. 
Let us consider some examples of them. 

Take first the rational numbers, which are the fractions represent- 
ing the ratio of one whole number to another. They can be written 
in a rectangular array thus: 



Mathematics and Logic 43 




They may now be arranged in a single order by taking the diagonals 
of this array in turn, thus: 

M, %, %, 91, %, %, %, %, %, %, %, 4 /3, 3 /4, %> %, ' ' ' 

When they are thus ordered, they can be put in a one-to-one corre- 
spondence with the natural numbers 

1, 2, \ 4, 5, 6, 7, . 

Any collection which can be put in a one-to-one correspondence 
with the natural numbers is said to be denumerable. Thus the ra- 
tional numbers form a denumerable or countable set. The cardinal 
number of a denumerable set is the smallest transfinite cardinal num- 
ber, and is denoted by Aleph-zero, 

Now let the rational numbers be arranged in order of magnitude 
and suppose that at a certain place in the order a division or cut 
is made, which causes the numbers to fall into two classes (e.g. all 
the rational numbers whose squares are less than 2 and all the 
rational numbers whose squares are greater than 2), which we shall 
call the left class and the right class, such that every rational number 
in the left class is smaller than every rational number in the right 
class. It may be that the right class has a least member, which will 
of course be a rational number, say p; or it may be that the left 
class has a greatest number, which will be a rational number, say q. 
In these cases the cut is said to be made by a rational number, p 
or q as the case may be. But if the left class has no greatest mem- 
ber and the right class has no least member, then the cut is still re- 
garded as being made by a number; but this will be a number of a 
new class, which is called an irrational number. Thus if the left and 
right classes are the rational numbers whose squares are respectively 
less and greater than 2, since there is no rational number whose square 



44 What Is Science? 

is exactly equal to 2, there will be an irrational number corresponding 
to the cut, and this is the number commonly represented by \/2. 
Rational and irrational numbers are both comprehended in the name 
real numbers. 

We have seen that the class of rational numbers is countable; but 
the class of real numbers, composed of rationals and irrationals to- 
gether, is not countable. To prove this, suppose it to be possible 
that all the real numbers from to 1 could be arranged in order 
as 1st, 2nd, 3rd, . . . etc., say n x , n 2 , n 3 , . . . Suppose that these 
numbers are represented in the ordinary denary scale as decimals. 
Then we can form a new decimal in the following way: take its first 
digit to be any digit (from to 9) different from the first digit of 
HI; take its second digit to be any digit different from the second digit 
of n 2 ; take its third digit to be any digit different from the third 
digit of n 3 ; and so on. The number thus formed differs from all 
the numbers previously enumerated and it is a real number between 
and 1; so the original enumeration cannot have contained all the 
real numbers between and 1. By this reductio ad absurdum we see 
that the set of real numbers from to 1 is not denumerable. 

The set of real numbers is called the arithmetic continuum; by 
what has just been proved, the transfinite cardinal number of the 
arithmetic continuum is not Aleph-zero, but a greater transfinite 
number, which is denoted by c. 

The arithmetic continuum has been constructed arithmetically, 
without any dependence on time and space, the two notions of the 
continuum with which we are intuitively familiar. If we are to as- 
sume that the arithmetic continuum is equivalent to the linear con- 
tinuum, so that the motion of a particle along the line is an exact 
image of a numerical variable increasing from one value to another, 
it is evident that we must introduce an axiom, namely that there is 
a single point on the line corresponding to every single real number. 
Of course we are not bound to assume this axiom. We may assume 
that several points, forming an infinitesimal segment, separate the 
right and left classes in the proposition by which irrational numbers 
were defined. On this assumption, the axiom of Archimedes, to which 
reference was made on page 37, would not be true. 

If the Pythagorean conception of the line as made up of unit 



Mathematics and Logic 45 

points had been correct, the ratio of any two segments of the line 
would have been a rational number, and there would have been no 
room for irrationals. 



The Number of Points in a Three-Dimensional Space 

One would naturally expect that the number of points in a three- 
dimensional region, such as the interior of a cube of side unity, 
would be infinitely greater than the number of points on a segment 
of a line, say one of the edges of the cube. But, surprisingly, this is 
not the case: the points in the cube can be made to correspond, 
point by point, with the points in its edge. 

For take three of the edges, meeting at one comer, as axes of 
co-ordinates x, y, z, so that for points in the cube we have three 
co-ordinates all between and 1. A point on an edge can be speci- 
fied by a single co-ordinate w between and 1. Now let the co- 
ordinate w, which represents a particular point on the edge be ex- 
pressed as a decimal, adding GTs at the end so as to make it an 
unending decimal. Take the 1st, 4th, 7th, etc. digits of w, and write 
down a decimal x of which these are the successive digits. Similarly 
write down y, consisting of the 2nd, 5th, 8th, . . . digits of \v, and 
write down z, consisting of the 3rd, 6th, 9th, . . . digits. The point 
of space whose co-ordinates (x, y, z) are thus determined corresponds 
uniquely to the value of w; thus, there is a one-to-one correspondence 
between the points on the edge and the points inside the cube, and 
therefore they have the same number. 



Imaginary Quantities 

A work written by an Egyptian priest more than a thousand years 
before Christ, with the alluring title "Directions for knowing all dark 
things," explains how to solve various numerical problems, such as 
"What is the number which, when its seventh part is added to it, 
becomes 24?" The ancient Babylonians also proposed arithmetical 
puzzles, and were acquainted with arithmetic and geometric pro- 



46 What Is Science? 

gressions. But algebra as a science can scarcely be said to have existed 
before the introduction of negative numbers in the early centuries 
of the Christian era, although results that are now commonly ob- 
tained by algebraic methods had long been known. 
The solution of the quadratic equation in algebraic notation 

ax 2 + bx + c = 

was achieved in geometrical form by the Greek mathematicians. If 
the quadratic has no roots which are real numbers, it possesses alge- 
braic roots of the form x + y V 1 where x and y are real: that is, 
roots that are complex quantities. But the geometrical preoccupations 
of the Greeks led to their attention being devoted entirely to real 
roots, and solutions involving the "imaginary" quantity \/l were 
dismissed by everybody before the sixteenth century as nonexistent. 
In the Renaissance, however, the Italian mathematicians discovered 
the solution of the cubic equation 



their formula gave for instance the solution of the equation 

x 3 -15x-4 = 
as 

x = # (2 + 11 V-l) +#(2 -11 V-l). 
In order to evaluate this, we note that 

2 + 11 V-l = (2 + V-l) 8 , and 2 -11 V-l = (2 - V-1) 8 - 
So we have the root expressed in the form 



or 

x = 4. 



We have thus found a real root of the cubic, by a calculation which 
cannot avoid using \/l; and, this discovery compelled the mathema- 
ticians to face the question of the status of imaginary quantities. For 
a long time their attitude was one of mystification: the imaginary 



Mathematics and Logic 47 

was, they said, inter Ens et non-Ens amphibium ("an amphibian 
between Being and non-Being" ) . 

Later it was shown to possess many important properties. Thus, 
many theorems were found to be true only when the numbers con- 
cerned were no longer restricted to be real: for instance, the theorem 
that every algebraic equation of degree n has n roots is true in 
general only when complex roots are taken into account. But con- 
servatism died hard. In the latter part of the eighteenth century an 
English mathematician, Francis Maseres, who had been senior wran- 
gler at Cambridge in 1752, published several tracts on algebra and 
theory of equations in which he refused to allow the use of "im- 
possible" quantities. 

Today, imaginary quantities are of great importance; in fact, the 
extensive and most useful Theory of Functions of a Complex Variable 
is wholly concerned with functions which depend on the quantity 
x + y V 1- It is a strange fact that as mathematics grows more ab- 
stract, it becomes more effective as a tool for dealing with the concrete 
a point that was often stressed by the philosopher A. N. Whitehead. 
As an example, one may cite the very abstract theory of groups, which 
has many applications in the modern quantum-mechanical physics. 



System of Numeration 

The choice of the number 10 as the basis of our system of numera- 
tion is due to our having ten fingers; among primitive peoples the 
set of fingers, in which ten objects are presented in a definite order, 
was the natural aid to counting. Modern systems of numeration de- 
pend on the notion of place-value, with the use of the symbol zero, 
a plan which seems to have been introduced about 500 A.D.: thus 
the number 5207.345 means 

5.10' + 2.10" + 0.10 + 7 + Ko + Mo 2 + 6 /io 8 . 

While the historical reason for the use of a decimal system is readily 
intelligible, it must be said that an octonary system, based on the 
number 8 ( so that 5207.345 would mean 

5.8* + 2.8' + 0.8 + 7 + % + ys 2 + %') 



48 What Is Science? 

would be more convenient. The multiplication table of the octonary 
system would call for only half as great an effort aj is required in 
the decimal system; and, the most natural way of dealing with frac- 
tions is to bisect again and again, as is done for instance with brokers' 
prices on the stock exchange. It is perhaps unfortunate that our re- 
mote ancestors, when using their fingers for counting, included the 
thumbs. 

Another system of numeration, which has become prominent in 
recent years, owing to its use in the modern electronic calculating 
machines, is to express numbers in "the scale of 2," or the "binary 
scale," in which 10110.01101 would mean 

2 4 22 2 y 2 2 i/ 2 3 + i/ 2 5. 



Symbolic Logic 

Long ago Leibnitz, in the course of his life as a diplomat, sometimes 
found himself required to devise a formula for the settlement of a 
dispute, such that each of the contending parties could be induced 
to sign it, with the mental reservation that he was bound only by 
his own interpretation of its ambiguities. Equivocation, such as was 
practiced in this connection, was, as Leibnitz well knew, impossible 
in mathematics, where every symbol and every equation has a unique 
and definite meaning. And the contrast led him to speculate on the 
possibility of constructing a symbolism or ideography, like that of 
algebra, capable of doing what ordinary language cannot do, that is, 
to represent ideas and their connections without introducing un- 
detected assumptions and ambiguities. He therefore conceived the 
idea of a logical calculus, in which the elementary operations of the 
process of reasoning would be represented by symbols an alphabet 
of thought, so to speak and envisaged a distant future when philo- 
sophical and theological discussions would be conducted by its 
means, and would reach conclusions as incontrovertible as those of 
mathematics. Perhaps this was too much to hope, but the actual 
achievements of mathematical logic have been amazing. Logic, when 
its power has been augmented by the introduction of symbolic 



Mathematics and Logic 49 

methods, is capable of leading from elementary premises of extreme 
simplicity to conclusions far beyond the reach of the unaided reason. 

The first outstanding contribution to the subject was made by 
George Boole, for the latter part of his life, professor in Cork, who 
published a sketch of his theory in 1847, and a fuller account in 
1854, in his book An Investigation of the Laws of Thought. In this 
system, a letter such as x denotes a class or collection of individual 
things to which some common name can be applied: for instance, 
x might represent the class of all doctors. We can also regard x as 
a symbol of operation, namely, the operation which selects, from the 
totality of objects in the world, those objects which are doctors. Now 
let y denote some other class, say the class of all women. Then the 
product xy must represent the result of first selecting all women, and 
then selecting from them those who are doctors; that is, xy represents 
all women doctors, all the individuals who belong both to the class x 
and to the class y. When, in ordinary language, a noun is qualified 
by an adjective, as in ''feminine doctor/' we must understand the 
idea represented by this product. 

Now consider the case when the class y is the same as the class x. 
In this case, the combination xy expresses no more than either of the 
symbols taken alone would do, so xy = x, or (since y is the same as x) 
x 2 = x. In ordinary algebra, the equation x 2 = x is true when x has 
either of the values zero and unity, but in Boolean algebra all symbols 
obey this law. 

Let us now take up the question of addition. The class x + y is 
defined to consist of all the individuals who belong to one at least 
of the classes x and y, whether the classes overlap or not. 

The symbol used for zero in ordinary algebra is used in Boolean 
algebra to denote the class that has no members, the null class: ob- 
viously we must have 

x = and x -f = x, 

as in ordinary algebra. 

The symbol 1 is used to denote the class consisting of everything, 
or the "universe of discourse": it has the properties 

x- 1 ~x and x-f- 1 = 1. 



50 What Is Science? 

Lastly, the minus sign must be introduced: the symbol x is de- 
fined to be the class consisting of those members of 1 which do not 
belong to x, so that 

xxl and 



So far, we have interpreted Boolean algebra as an algebra of classes; 
but, we may take the classes to be classes of cases in which certain 
propositions are true, and this led to an interpretation of it as an alge- 
bra of propositions. If x and y are propositions, their product would 
represent simultaneous affirmation, so xy would be the proposition 
which asserts "both x and y": the sum would denote alternative af- 
firmation, so x + y would be the proposition "either x or y or both." 
The minus sign would represent "it is not true that," so x would 
be the proposition contrary to x: the equation x ~ 1 would imply 
that x is true, while the equation x =1, which is equivalent to 
x = 0, would signify that x is false. The equation x -f- x = 1 would 
now represent the logical principle of the excluded middle, that every 
proposition is either true or false, and the equation x- ( x) ~0 
would represent the principle of contradiction. 



Peano's Symbolism 

Boole used only the ordinary algebraic symbols: the symbol x, which 
in ordinary algebra represents multiplication, may be said to corre- 
spond in Boolean algebra to the word and, while the symbol of addi- 
tion, -f-, corresponds to or, and the symbol of a negative quantity, 
, corresponds to not. The great development of such ideas took 
place in the last years of the nineteenth century, when Giuseppe 
Peano, professor at the University of Turin, invented a new ideogra- 
phy for use in symbolic logic. He introduced new symbols to rep- 
resent other logical notions, such as "is contained in," "the aggregate 
of all x's such that," "there exists," "is a," "the only," etc. For exam- 
ple, the phrase "is the same thing as" is represented by the sign =, 
while the symbol r\ between two classes indicates the aggregate of in- 
dividuals who belong to both classes (the product of Boole's algebra). 
One of the elementary processes of logic consists in deducing from 



Mathematics and Logic 51 

two propositions, containing a common element or middle term, a 
conclusion connecting the two remaining terms. This corresponds 
to the process of elimination in algebra and may be performed in a 
way roughly analogous to it. The parallelism of logic and algebra is 
indeed far reaching: for instance, the logical distinction between 
categorical propositions and conditional propositions corresponds 
closely to the algebraical distinction between identities and equations. 
Again, the inequalities of algebra have their analogues in logic. Con- 
sider, for instance, the statement that if a proposition a implies a 
proposition fc, and b implies a proposition c, then a implies c. This 
bears an obvious resemblance to the algebraical theorem that if a is 
less than ft, and b is less than c, then a is less than c. It is useful to have 
a symbol which represents logical implication or inclusion, and all 
modern forms of symbolic logic do in fact employ one or two, one in 
the calculus of propositions and one in the calculus of classes. This 
however, does not represent an independent concept, but can be de- 
fined in terms of the logical product; for the statement that a is in- 
cluded in, or implies, ft, is equivalent to the statement that the 
logical product of a and b is equal to a. 

Peano's ideograms represent the constitutive elements of all the 
other notions in logic, just as the chemical atoms are the constitutive 
elements of all substances in chemistry; and they are capable of re- 
placing ordinary language completely for the purposes of any deduc- 
tive theory. 



The Developments of Whitehead and Russell 

In 1900 A. N. Whitehead and Bertrand Russell, both of Cambridge, 
went to Paris to attend the congresses in mathematics and philosophy 
which were being held in connection with the International Exhibi- 
tion of that year. At the Philosophical Congress they heard an ac- 
count of Peano's system and saw that it was vastly superior to any- 
thing of the kind that had been known previously. They resolved 
to devote themselves for years to come to its development, and, in 
particular, to try to settle by its means the vexed question of the 
foundations of mathematics. 



52 What Is Science? 

The thesis which they now set out to examine, and if possible to 
prove, was that mathematics is a part of logic: it is the science con- 
cerned with the logical deduction of consequences from the general 
premises of all reasoning, so that a separate "philosophy of mathemat- 
ics" simply does not exist. This of course contradicts the Kantian doc- 
trine that mathematical proofs depend on a priori forms of intuition, 
so that, for example, the diagram is an essential part of geometrical 
reasoning. Whitehead and Russell soon succeeded in proving that the 
cardinal numbers 1, 2, 3, ... can be defined in terms of concepts 
which belong to pure logic, such as class, implication, negation, and 
which can be represented by Peano ideograms. From this first suc- 
cess they advanced to the investigations published in the three colos- 
sal volumes of Principia Mathematica, which appeared in 1910-1913 
and contain altogether just under 2,000 pages. 

It was admitted that for mathematical purposes certain axioms 
must be adjoined to those that are usually found in treatises on logic, 
e.g., the intuition of the unending series of natural numbers, which 
leads to the principle of mathematical induction; but this extension 
of logic did not affect the main position. 

The growth of logic, which had been at a standstill for the two 
thousand years from Aristotle to Boole, has progressed with amazing 
vitality from Boole to the present day. It is remarkable that some of 
the errors of Aristotle remained undetected until the recent develop- 
ments. Consider, for instance, his doctrine that "in universal state- 
ment the affirmative premise is necessarily convertible as a particular 
statement, so that for example from the premise all dragons are 
winged creatures, follows the consequence some winged creatures are 
dragons. The premise is unquestioned, but Aristotle's deduction from 
it asserts the existence of dragons. Now it is evident that the existence 
of dragons cannot be deduced by pure reason and, therefore, Aris- 
totle's general principle must be wrong. The most important advance, 
however, was not the detection of the errors of the old logic, but the 
removal of its limitations. The Aristotelian system in effect took into 
account only subject-predicate types of propositions, and failed to 
deal satisfactorily with reasoning in which relations were involved, 
such as "If there is a descendant, there must be an ancestor/' It was 



Mathematics and Logic 53 

not possible to reduce to an Aristotelian syllogism the inference that 
if most have coats and most have waistcoats, then some must have 
both coats and waistcoats. In this and other respects the subject has 
become enlarged to such an extent that only a comparatively small 
part of any modern treatise is devoted to the traditional logic. 

Whitehead and Russell's work may without exaggeration be de- 
scribed as the foundation of the modern renaissance in logic, which, 
as the successive volumes of the Journal of Symbolic Logic show, is 
now chiefly centered in America. A notable feature of it is the devel- 
opment of what Hilbert has called metamathematics y that is, of the- 
orems about theorems. An example is the result found in 1931 by 
Godel, that there are some propositions of mathematics which, though 
they have a meaning, cannot be either proved or disproved by means 
of any system based on axioms, such as that of Principia Mathematica. 

Russell's Paradox 

The advantages of an ideography as compared with ordinary language 
are strikingly evident in the discussion of certain contradictions which 
have threatened to invalidate reasoning, such as a famous paradox 
that was discovered fifty years ago by Bertrand Russell. He remarked 
that in the case of e.g., the class whose members are all thinkable con- 
cepts, the class, being itself a thinkable concept, is one of its own 
members. This is not the case with e.g., the class of all blue objects, 
since this class is not itself blue. We can therefore say that those 
classes which do not contain themselves as one of their members form 
a particular kind of classes. The aggregate of these classes constitutes 
a new class which we shall call x. Let us put this definition in the two 
forms: 

Form A. A class which contains itself as a member is not a member 
ofx. 

Form B. A class which does not contain itself as a member is a 
member of x. Now if x were a member of itself, then by A it would 
not be a member of itself, so we should have a contradiction; while 
if x were not a member of itself, then by P it would be a member 
of itself, which is again a contradiction. Thus on either supposition 



54 What Is Science? 

we arrive at a contradiction, which appears to be insoluble by any 
kind of verbal explanation. 

Now let us look at the matter from the point of view of symbolism. 
The contradiction that "x is an x" is equivalent to "x is not an x" 
was obtained essentially by substituting x for y in the statement that 
(1) y is a class (2) y is an x, is equivalent to "y is not a y." This 
substitution, however, is not, as it stands, an operation performed on 
the fundamental logical symbols in accordance with the rules which 
are laid down for operating on them; for, x is not itself one of the 
elementary ideograms, but is an abbreviation, a single letter standing 
proxy for a complex of ideas. Now all abbreviations, however con- 
venient, are from the logical point of view superfluous; and an argu- 
ment involving them is not valid unless, at every stage of it, the 
proxy symbols can be replaced by the full expressions for which they 
stand. In order therefore to be sure that what has been done is cor- 
rect from the point of view of symbolic logic, we must translate the 
whole argument, and in particular the operation of substituting x for 
y, into the language of the elementary ideograms and the operations 
that are permissible with them, so that all explicit mention of x will 
have been eliminated from the proof. When, however, we try to do 
this, we find that we cannot. It is not possible to state Russell's para- 
dox in the form of an assertion composed solely of the elementary 
ideograms. This shows that if we had from the beginning avoided the 
use of ordinary speech or of proxy symbols and conducted all our 
investigations according to the strict precepts of ideography, then 
Russell's paradox would never have emerged. It can be obtained by 
argumentation in words, or it can be obtained by a quasi-symbolic 
argument in which an operation is permitted which is untranslatable 
into pure symbolic logic; but it cannot be obtained by any process 
which is restricted to using throughout nothing but the elementary 
ideograms and the operations that are recognized as permissible with 
them, and which express both the final result and all intermediate 
equations in terms of them exclusively. Thus Russell's paradox, being 
inexpressible in symbolic logic, is really meaningless, and we need not 
concern ourselves with it further. The contradiction which appears in 
it is not inherent in logic, but originates in the imperfections of lan- 
guage and of abbreviated symbolism. 



Mathematics and Logic 55 

The Inflationists 

The Whitehead-Russell doctrine that mathematics is based on logic 
is opposed by a school led by the Dutch mathematician L. E. J. 
Brouwer and the German Hermann Weyl, and known as intuition- 
ists, who maintain the contrary view, that logic is based on mathe- 
matics. The series of natural numbers is held to be given intuitively 
and to be the foundation of all mathematics, so that numbers are not 
derived, as Russell supposed, from logic. Their system contains a new 
feature which may be explained thus. 

Let it be asked whether, in the development of * as a decimal frac- 
tion, there is a place where a particular digit, say 5, occurs ten times 
in succession. It is of course conceivable that by performing the 
actual development we might come upon such a succession; or it is 
conceivable that a general proof might show that it cannot happen; 
but these two solutions evidently do not exhaust all the possibilities. 
Under these circumstances, Brouwer and Weyl decline to pronounce 
the disjunctive judgment of existence, that the development of v as 
a decimal either does or does not include a succession of ten 5's; in 
other words, they assert that the logical principle of the excluded mid- 
dle, that every proposition is either true or false, is not valid in do- 
mains where a conclusion one way or the other cannot be reached in 
a finite number of steps. They replace the notion of true by verifiable 
and call propositions false only if their contradictory is verifiable. This 
position leads them to abandon the attempt to justify large parts of 
traditional mathematics: in particular, they reject all proofs by re- 
ductio ad absurdum (which generally depend on the law of the ex- 
cluded middle) and all propositions involving infinite collections or 
infinite series. The disastrous consequences to mathematical analysis 
of adopting such a position have prevented it from gaining any gen- 
eral acceptance, but it is not easy to disprove. 

Probability 

In 1654 some one proposed to Blaise Pascal the following problem: 
a game between two players of equal skill is discontinued for some 



56 What Is Science? 

reason before it is finished: given the scores attained at the time of 
the stoppage, and the full score required for a win, in what propor- 
tion should the stakes be divided? Pascal communicated the prob- 
lem to his friend Pierre de Fermat, and the two in finding the solu- 
tion created the theory of probability. 

Like any other branch of pure mathematics, the theory of proba- 
bility begins with undefined notions, and axioms. We consider a 
trial, such as drawing a card out of a pack, in which different possible 
events (the drawing of particular cards) might occur, and we intro- 
duce the undefined notion of probability, which may be described as 
a numerical measure of quantity of belief that one particular event 
will happen, i.e., that some named card will be drawn. The axiom 
on which the theory is based may be stated thus: In a given trial let A 
and B be two events -which cannot possibly happen together; then 
the probability that either A or B will happen is the sum of the prob- 
abilities of their happening separately. 

Thus in tossing a coin, let x be the probability of heads and y the 
probability of tails. Then on account of the symmetry of the coin 
we may assume that x = y. Moreover, from the axiom we see that 
x -\- y is the probability that cither heads or tails will fall; but this 
latter is a certainty, to which we give our entire belief. It is convenient 
to measure entire belief by the number unity: so we have 

x ~ y x + 7 1 

and therefore x y = %. The probability of heads in a single toss 
of a coin is l / 2 . 

In practically all the calculations that we can make, some use is 
made of a property of symmetry: thus, a die is a cube, symmetrical 
with respect to all its six faces, so the probability that when cast it 
will show a particular specified face is %; a pack has 52 cards which 
are equally likely to be drawn, so the probability of drawing, say, the 
ace of spades, is % 2 - 

The axiom can readily be extended in the form: the probability of 
an event is the ratio of the number of favorable cases to the number 
of possible cases, -when all cases are supposed (generally for reasons 



Mathematics and Logic 57 

of symmetry) to be equally likely. Thus, suppose an old man has only 
two teeth: what is the probability that they will meet? In this case, 
whatever position one of the teeth occupies, there are 31 possible 
positions for the other tooth, and of these only one is favorable. There- 
the required probability is 3 /si. 

It is, however, easy to make mistakes through not taking sufficient 
care in enumerating the equally likely cases. Thus, take the follow- 
ing argument, which appeared in a recent book: ''The sum of an 
odd number and an even number is an odd number, while the sum 
of two odd numbers is an even number, and so is the sum of two 
even numbers. Hence if two numbers are chosen at random, the prob- 
ability that their sum will be even is twice the probability that it will 
be odd." The error here comes from not recognizing that there are 
four equally likely cases, namely, OO, OE, EO, EE; of these, two are 
favorable to an even sum and two to an odd sum, so the probabilities 
of an odd and an even sum are really equal. 

A well-known problem is that of the "Yarborough," i.e., the proba- 
bility that a hand, which is obtained when an ordinary pack of cards 
is dealt between four players, should contain no card higher than a 
nine. The probability is nearly-y^-; a former Earl of Yarborough is 
said to have done very well for himself by betting 1000 to 1 against 
its happening. 

Although the difficulty of probability problems as regards mathe- 
matical symbolism is usually not great, they are often very puzzling 
logically. The reader may like to try the following: given an assertion, 
A, which has the probability a, what does that probability become, 
when it is made known that there is a probability m that B is a 
necessary consequence of A, B having the probability b? l 

A problem which has some bearing on the credibility of evidence 
is the following: let p be the a priori probability of an event which a 
witness has asserted to have happened; and let the a priori probabil- 
ities that he would choose to assert it be v on the supposition of its 
being true, and \v on the supposition of its being false. What, after 

'The answer is: a [1 m(l b)] 

l-am(l-b) 



58 What Is Science? 

his assertion, is the probability that it really happened? The answer 
is 

pv 



pv+ (1 p) w 

We see that however small p may be, the value of this fraction may 
approach indefinitely near to unity that is, the probability that the 
event happened may approach certainty provided w be much less 
than v: Hiat is, provided the fact of the assertion may be much 
more easily accounted for by the hypothesis of its truth than of its 
falsehood. We must not let ourselves be influenced unduly by the 
antecedent improbability of an event but must think out the conse- 
quences of the contrary hypothesis, which may be more improbable 
still. 



Statistics 

One of the most important applications of the theory of probability 
is to questions regarding statistics, which have to be dealt with 
specially by actuaries, astronomers, and social workers. The connec- 
tion between probability and statistics is indicated by a theorem es- 
tablished in 1713 by James Bernoulli, which may be thus stated: let 
p be the probability of the happening of an event in a single trial, and 
let s be the number of times the event is observed to happen in n tri- 
als, so -^- may be called the statistical frequency; then as n increases 
indefinitely, the probability approaches certainty that the statistical 
frequency mil approach p. 

This law suggests that we should study what happens when the 
number of trials is limited, though great, and should calculate the 
probability of the deviations of the statistical frequency from p which 
then occur. The calculation is not difficult, and leads to definite laws 
of frequency of error. These are the basis of the methods used e.g. in 
astronomy for combining observations so as to find the most prob- 
able value of a set of quantities from a number of discordant observa- 
tions of them. 

If an event happens only rarely, the formula for the probability of 



Mathematics and Logic 59 

s occurrences in n trials is different. It has been verified by compari- 
son with the statistical frequency in such different cases as the num- 
ber of deaths from the kicks of horses in the Prussian Army, and the 
number of alpha-particles falling on a screen in unit time in certain 
experiments with radioactive substances. 

The theory of statistics is much concerned with what is called 
correlation, which may be explained thus. Consider a definite group 
containing a large number of men and let x be some measurable at- 
tribute of a man, say his height, while y is another measurable attri- 
bute, say his weight. Let the values of these attributes for a man be 
indicated by a dot whose co-ordinates are x and y in a diagram. The 
dots corresponding to all the men will cluster round a certain point O 
which represents the mean height and weight. Now take axes O x , O 7 , 
through O. We know that in general a tall man will also be a heavy 
man, and therefore a positive deviation of x from the mean will most 
often be associated with a positive deviation of y, and similarly a neg- 
ative deviation of x will generally be associated with a negative devia- 
tion of y. 



V '/ * 



>* 



That is to say, the dots will lie chiefly in the first and third quadrants 
of the diagram. In such a case we say that there is correlation be- 
tween the two attributes x and y. It can be measured by a coefficient 
of correlation, whose value can be calculated by forming the sums of 
the values of x f , y*, and xy, for all the points in the diagram. 



60 What Is Science? 

Stochastic Systems 

The principle of causality is expressed by the assertion that whatever 
has begun to be, must have had an antecedent or cause which ac- 
counts for it. This principle is not violated by events of the kind that 
has usually been studied in works on probability. Consider for in- 
stance the tossing of a coin: we do not know on which side the coin 
will come down, but that is because we do not know all the circum- 
stances of its projection the mass and shape of the coin, the force 
applied by the thumb of the operator, etc. We do not doubt that if 
all these data were available to us, it would be theoretically possible 
to calculate completely the behavior of the coin, and to predict the 
side on which it would come down; and, therefore, our lack of ability 
to make this prediction is due only to our ignorance and not to any 
failure of determinism in nature. Systems whose working is really 
governed by strict law, but whose performance we cannot foretell 
for want of knowledge, are said to have hidden parameters: if we 
knew all about the hidden parameters, we should be able to predict 
everything. 

In the newer physics, we have phenomena like the spontaneous 
breakup of a radium atom, in which an alpha-particle is given off and 
the atom is transformed into an atom of radium emanation. It is not 
possible to foretell the instant when any particular radium atom will 
disintegrate; and, it was formerly supposed that this is because a 
radium atom contains hidden parameters perhaps the positions and 
velocities of the neutrons and protons inside the nucleus which are 
not known to us and which determine the time of the explosion. For 
reasons which belong to physics and therefore would not be in place 
here, it is now generally recognized that these hidden parameters 
do not exist. The disintegrations do not occur in a deterministic 
fashion, and the only knowledge which is even theoretically possible 
regarding the time of disintegration is the probability that it will hap- 
pen within (say) the next year. A system in which events such as 
disintegrations take place according to a law of probability, but are 
not individually determined in accordance with the principle of caus- 
ality, is said to be a stochastic system. The fact that the systems coc- 



Mathematics and Logic 61 

sidered in microphysics are largely stochastic systems make the the- 
ory of probability of fundamental importance in the application of 
mathematics to the study of nature. 



Conclusion: The Philosophy of Mathematics and the 
Philosophy of Science 

This talk on mathematics may end with an attempt to answer the 
question, how is progress in mathematics related to progress in the 
other sciences? 

We have seen that a very high standard was attained in mathe- 
matics as early as the fourth and third centuries before Christ; the 
Elements of Euclid are sufficient to carry the modern student of 
geometry to the point where university courses begin. No comparable 
development was reached in any other branch of science for 2000 
years. Why was this? 

In the generation immediately before Euclid, as we have seen, the 
philosopher Aristotle, whose scientific interests were in biology rather 
than in mathematics, tried to find a general method of adding to 
knowledge, by creating the science of logic, which he brought to the 
form in which it remained with little change until the present age. In 
showing how logic might be used to advance discovery, Aristotle 
relied chiefly on the syllogistic type of reasoning that had been so 
successful in geometry. But syllogisms must start from certain basic 
truths which are accepted as premises; and it was in the methods of 
finding these basic truths that Aristotle's scheme was weakest. He 
collected a great number of observations but does not seem to have 
taken care to reject those that could not be verified, and he never 
designed an experiment for the purpose of testing a hypothesis. Syl- 
logisms are as a rule comparatively unimportant in the nonmathe- 
matical sciences, and the great place given to them in logic led the 
later Aristotelians to attach undue importance to mere words. 

In the thirteenth century, the influence of Aristotle was greatly 
increased by the work of St. Thomas Aquinas; but, so far as science 
was concerned, Aristotelianism developed in a completely sterile form 
and a violent reaction against it set in, the leaders of which were 



62 What Is Science? 

Galileo (1564-1642) and Bacon (1561-1626). Bacon emphasized 
the importance of induction from observation and the necessity for 
experiment, though even in Bacon we do not find any recognition of 
the necessity for framing hypotheses and then designing experiments 
to test them. This indeed can hardly be said to have figured as a 
doctrine of philosophers until it had become the practice of the great 
men of science of the seventeenth century, particularly of Isaac New- 
ton (1642-1727). The outstanding characteristic of the Newtonian 
philosophy was its focusing of interest on the changes that occur in 
the objects considered. The Greek philosophers had marked the dis- 
tinction between mathematics and physics by assigning to the mathe- 
matician the study of entities which are conserved unchanged in 
time, and to the physicist the study of those entities which undergo 
variations; but Newton created a type of mathematics in which the 
calculation of rates of change was fundamental. The rate of change 
of position of a body moving in a straight line, which is called its 
velocity, and the rate of change of the velocity, which is called its 
acceleration, were now studied. Newton regarded a curve as gener- 
ated by the motion of a point, a surface by the motion of a curve, 
and so on. The quantity generated was called the fluent, and the 
motion was defined by what he called the fluxion; and he showed 
that when a relation was given between two fluents, the relation be- 
tween their fluxions could be found, and conversely. This theory of 
fluxions, known later as the infinitesimal calculus, became the major 
occupation of the mathematicians of the eighteenth and nineteenth 
centuries, and led to wonderful advances in the study of nature. 



ASTRONOMY AND 
COSMOLOGY 

HERMANN BONDI 



about 

Hermann Bondi 



Hermann Bondi was born in Vienna in 1919. Pie lived there until 
1937 y attending school and showing great interest in mathematics 
and physics. In 1937 he went to Trinity College, Cambridge, to 
study mathematics. As an Austrian subject he was interned in 1940, 
just as he obtained his B.A. degree. After his release he returned to 
Cambridge for a short period as research student and spent the re- 
mainder of the war in the admiralty, doing research on radar. During 
this period of more than three years he was in constant contact with 
Fred Hoyle, whose keen interest in problems of astronomy and astro- 
physics did much to change Bondi s main line of work from classical 
applied mathematics (waves and hydrodynamics) to theoretical as- 
tronomy. Hoyle and Bondi were joined shortly afterward by Thomas 
Gold, and together the three men discussed astrophysical questions 
"during every free hour of the day and late into the night! 1 The work 
done during these years led to Bondi s election to a fellowship at 
Trinity College in 1943. After the war Bondi, Gold and Hoyle re- 
turned to Cambridge and joined R. A. Lyttleton who had been 
working on similar problems at Princeton and in Cambridge before 
the war. 

In collaboration with one or two members of this group, Bondi 
published numerous papers on astronomical and geophysical ques- 
tions, notably the effect of interstellar gas clouds on stars. He is es- 
pecially well known for the steady-state theory of the expanding uni- 



about Hermann Bondi 65 

verse, proposed jointly by him and Gold in 1948, and since then 
widely discussed. The theory is described in the followmg essay. In 
1952 he published a book on cosmology which, while quite difficult 
in spots, can be recommended to the thoughtful reader as the clear- 
est summary of its kind. 

After many years in Cambridge as university lecturer in mathe- 
matics and as Fellow of Trinity College, Bondi moved to King's Col- 
lege, London, in 1954 as professor of mathematics. 

Bondi is married and has three children. His wife, herself a mathe- 
matics graduate interested in astronomy and particularly in the con- 
stitution of the stars, has published papers in this field, individually 
and jointly with her husband. The Bondis have paid several visits to 
the United States. In 1951 they were for three months at Cornell 
University, where he was a research associate of the Laboratory of 
Nuclear Studies. More recently they spent the fall of 1953 at Harvard 
College Observatory and Bondi also gave a course of Lowell Lectures 
in Boston. 

In addition to his professional interest in theoretical science, Bondi 
is, in his own words, "very keen on the application of physics and 
engineering to the amenities of everyday life. The subjects of domestic 
heating (sadly neglected in England), transport, well-designed toys 
all interest me greatly" He is now designing a house in the country,. 
but within convenient reach of his new teaching post in London. 



ASTRONOMY AND COSMOLOGY 



HERMANN BONDI 



1. Probably the most intriguing feature of astronomy is the total 
inaccessibility of its objects of study, the celestial bodies. All astro- 
nomical information is derived from the examination of visible light 
and similar radiation (ultraviolet light, radio waves). It is a remark- 
able testimony to the efficiency of the scientific methods employed 
that a large amount of knowledge rests on apparently so scanty a 
source of information. 

The subject matter of astronomy may conveniently be divided into 
four fields in increasing order of the scales of size and distance: 

a. The solar system (the planets, satellites and smaller bodies) and 
its arrangement and origin. 

b. The "fixed" stars, their individual properties and close associa- 
tions. 

c. The organization of the stars and of other matter into distinct 
separate galaxies, each of them containing between a billion and 
a hundred billion stars. 

d. The arrangement, past, present and future, of the galaxies in 
the universe. This subject is known as cosmology. 

In a brief survey such as this it would seem most desirable to pick 
out a particular development in each field and to discuss the signifi- 
cance of the questions raised and arguments used. 

66 



Astronomy and Cosmology 67 

2. The growth of our knowledge of the motion of the planets 
raises several interesting considerations. The peculiar behavior of the 
planets in moving across the background of other stars attracted at- 
tention in very early times. First came the observation and descrip- 
tion of the motions of the objects; then attempts were made to con- 
struct models which, though based on simple geometrical concepts, 
exhibited the complex observed behavior. The model of Copernicus, 
which put the sun at the center and supposed the planets to go in 
circles around it, was simpler and hence superior to the model of 
Ptolemy, in which the earth occupied the central position. Kepler 
refined and elaborated the Copernican model by showing that the 
planets moved in ellipses rather than in circles and by establishing 
the rules applicable to their orbital speeds. The next great step was 
taken by Newton. 

It is well known that Newton, on observing an apple fall, specu- 
lated on whether the same force that pulled the apple down to 
earth also kept the moon in its orbit round the earth, and the earth 
in its orbit round the sun. By assuming that it did, he was emi- 
nently successful in describing all motions taking place within the 
solar system. Although this story is familiar, an analysis brings out a 
number of the characteristic lines of thought of modern astronomy. 

The observation that an apple falls to the ground is a terrestrial 
observation. It describes an experiment that we can carry out at will 
in our surroundings, an experiment the result of which is described 
by Galileo's laws governing the free fall of bodies. It is a bold step to 
suggest that these laws of terrestrial physics apply also to distant 
bodies such as the moon. The underlying assumption is that our 
locally established laws of physics are of universal validity. It is typical 
of scientific activity that assumptions are made, where necessary, of 
such a kind that they are useful in extending the field of scientific 
endeavor, and are liable to observational disproof. The sole purpose 
of scientific theories is to bring existing observational results under 
one head and to forecast the results of future observations. If a theory 
does not attempt to do this it cannot be disproved. Accordingly it is 
scientifically valueless and hence is not a scientific theory. To the 
question "But how do you know that the law of gravitation really 
applies out there?" the scientist can only answer, "I do not fcnow, 



8 What Is Science? 

but I have found it useful to assume that it does. When I assume it 
to apply, I am able to correlate old, and to forecast new, observa- 
tions. Should my forecasts fail, the assumption would be disproved. 
This may happen any day, but until it is disproved I shall stick to the 
assumption as the most useful position I can take." 

Belief in the universal validity of terrestrial physics is related to 
Copernicus' model. For if the earth were a special sort of place, with 
the sun, the planets, and the stars turning round it, we could not 
expect it to be also a typical place. It is only because, following 
Copernicus, we suppose the earth to be typical rather than special, 
that we can assume terrestrial knowledge to be valid everywhere. 

Another highly significant feature of Newton's work is that he 
divided the whole set of questions relating to the solar system into 
two classes. The question "Given Jupiter's present position and ve- 
locity, where will it be six months from now?" does not appear in- 
trinsically any simpler than the question "Why is Jupiter further from 
the sun, and why is it bigger, than Mars?" Newton's theory of gravi- 
tation, while supplying a complete answer to questions of the first 
kind, does not even attempt to answer questions of the second kind. 
It is by no means obvious that this sort of splitting-up of a set of 
natural phenomena is at all possible. In many problems of physics 
one is faced with the necessity of deciding, before one starts to form 
a theory, whether some aspects of the phenomenon can be explained 
in isolation, without having to discuss other aspects of the same 
phenomenon. Thus Newton had to suppose that the gravitational 
attraction of the earth could be described independently of any 
knowledge of the chemical composition of the earth's interior. The 
flow of air round the wing of an airplane can similarly be discussed 
without examining the composition of the material of the wing, the 
sag of a bridge under a load of given weight and location without 
knowledge of the nature of the load. On the other hand the resolving 
power of a microscope or telescope cannot be discussed without tak- 
ing account of the wave nature of light, nor can the time lag in the 
lighting of a fluorescent bulb be discussed without considering the 
existence of cosmic radiation. 

Newton's work on the solar system showed that such divisions, 
so extremely useful to the investigator, were indeed possible. He was 



Astronomy and Cosmology 69 

able to show, at least in principle, how all future motions in the solar 
system could be found, once the position, velocity, and mass of each 
member were known at one instant of time. However, the question 
of why just these masses, positions, and velocities exist in the solar 
system was not examined at all, but was assimilated to the broader, 
much discussed, but largely unsolved problem of the origin of the 
solar system. Thus, while the motion of the moon can be predicted 
for centuries, we regard it as purely accidental (i.e., due to causes too 
remote and insignificant to examine) that the apparent sizes of the 
moon and sun are so nearly equal that both total and annular eclipses 
can occur, i.e., those in which the moon wholly obscures the sun, and 
those in which the angular diameter of the moon is a little smaller 
and the entire rim of the sun is visible when the center is blotted out. 

3. The utility of the law of gravitation is not confined to the solar 
system. In looking far afield, at the stars proper (the nearest star is a 
quarter of a million times as far from us as the sun) one observes 
pairs of stars moving around each other very slowly (in periods of a 
century or so); and also cases in which the spectroscopic analysis of 
the light of a star shows that it comes from two sources alternately 
approaching and receding, in periods of a day or so. Ascribing the 
motions of these so-called binary stars to mutual gravitation is a big 
jump from the theories which fit Newton's apple, but the results ob- 
tained by doing so are self-consistent and lead to the general notion 
of stellar masses of the same order of magnitude as the sun. In this 
way a number of stellar masses have been determined. 

The applications of terrestrial physics to distant regions are not 
limited to the law of gravitation. A successful theory of the constitu- 
tion of the stars has been developed. This is especially remarkable 
when it is considered that while we have some, though only limited, 
direct knowledge of the surface of the stars, a theory of their interior 
must necessarily be wholly inferential. 

Before discussing this remarkable theory itself, its setting and pur- 
pose must be made clear. What observational evidence does the 
theory of stellar constitution seek to correlate with ordinary physics? 
A somewhat lengthy description of this is required before the analysis 
of the methods of the theory can be resumed. 



70 



What Is Science? 



Through powerful telescopes enormous numbers of stars can be 
seen, but relatively few can be examined in sufficient detail to supply 
evidence useful for the theory. We must proceed by inferred evi- 
dence. Owing to the earth's motion round the sun, the nearest 
stars appear to describe in the course of a year a small circle 
against the background of more distant stars (Fig. 1). If this circle is 



Backfrocmd* 



distant 
start 




Earth's orbit 



Fig. 1 Measurement of the distance of a near star by observing its 
apparent annual motion. 

large enough, its angular radius can be measured and then the dis- 
tance of the star is known in terms of the radius of the earth's orbit. 
For the nearest star the angular radius of the circle is less than 1 
second of arc (1 inch at a distance of 4 miles), and angles down to 
about l /2o of this are measurable. In this manner the distances of 
several hundred stars have been established. The measurement of the 
intensity of the light received from the star, combined with the 
knowledge of its distance, allows the rate at which the star sends out 
light, its so-called intrinsic luminosity, to be determined. 

Many stars provide enough light for a spectroscopic analysis. This 
furnishes a great deal of valuable information, including data from 
which the line-of-sight velocity of the stars can be inferred 1 and a 
rough estimate made of the relative abundance of elements (and 
sometimes even isotopes) in the surface of the star. For our purposes 

1 The spectrum of the light received from * receding source is shifted to the red 
by an amount proportional to the velocity of recession, and conversely the jpec- 
trum of an approaching source is shifted to the violet. This effect, the so-called 
Doppler shift, can be measured owing to the existence of well-defined dark lines 
of known position in the spectra of the stars. The shift is of great importance in 
cosmology. 



Astronomy and Cosmology 



71 



the most important information afforded by the spectroscope covers 
the surface temperature of the star. The surface temperature deter- 
mines not only the color (red-hot, white-hot, etc.), from which, in- 
deed, the temperature is inferred, but also the rate of emission of 
light per unit area. Here we make use of a firmly established law of 
terrestrial physics. If the intrinsic luminosity of a star is known, as 
well as the luminosity per unit area, the surface area of the star may 
be deduced. Making the plausible assumption that stars are at least 
approximately spherical in shape, the radius of the star can now be 
found. 




Blue White Yellow Red 

Fig. 2 The color-luminosity diagram. 

The stars for which these data of surface temperature and intrinsic 
luminosity are known may be represented by points in the so-called 
luminosity-temperature or Hertzsprung-Russell diagram (Fig. 2). In 
this diagram brightness is represented by the height of the point 
above the base line; while the coolest (that is reddest) stars are 
plotted on the right, with the medium-hot (yellow to white) stars in 
the middle and the hottest (white to blue) on the left. 

It turns out that the representative points of the stars follow a very 
definite pattern. The large majority (95%) of the points fall into a 
narrow band stretching from the bottom right corner (faint red 
stars) to the top left (bright blue stars). This band is known as the 
main sequence and stars belonging to it may be referred to as normal 



72 What Is Science? 

stars. The implication of this pattern of the diagram is that for these 
stars the radius is a definite function of the luminosity. The main 
sequence is much more heavily populated in the lower fainter part 
than in the upper brighter part. Our own sun is in the middle part of 
the main sequence. Most stars are fainter (down to, say, Viooth of the 
brightness of the sun) and though relatively few are brighter, there 
are a very few extremely bright stars (up to possibly 50,000 times the 
luminosity of the sun) . 2 

It should be remembered that it is very difficult to see faint stars 
and relatively easy to see bright ones, even if they are far away. Full 
corrections for this powerful factor of observational selection are hard 
to make, so that our knowledge of the relative abundance of differ- 
ent types of stars is somewhat approximate and the lower limit (if 
any) of stellar luminosity is not properly known. 

In addition to the band of the main sequence certain other regions 
of the diagram are also populated, though large parts of the plot are 
quite empty. Bright red stars ("red giants") are found, which are 
represented in the upper right-hand part of the diagram, and ex- 
tremely bright stars of all colors seem to exist ("supergiants"). There 
is also a fairly compact group of faint stars of high surface tempera- 
ture and hence very small radii ("white dwarfs"). However, stars of 
about the same brightness as the sun seem to have necessarily about 
the same surface temperature as the sun. 

Brief mention must now be made of another diagram that can be 
drawn to represent observational results. This is the mass-luminosity 
diagram (Fig. 3). It has been explained how the masses of some stars 
can be found. If the luminosities of these stars are plotted against 
their masses it is found that there is a high degree of correlation be- 
tween these two quantities. Though the observations are poorer in 

"None of these tremendous stars are near us and their distance must be inferred 
by indirect means rather than by the method described above. These means gen- 
erally depend on the association in a group or cluster of the big star with a star 
of spectroscopically known type and hence of known intrinsic luminosity. The 
distance of this star can then be inferred from the known law of weakening of 
light with distance. Since the stars are associated, the big star will be at about the 
same distance. Alternatively, a favorable binary system may permit the masses and 
radii of its components to be measured with such accuracy that the type of star 
can be identified and its intrinsic luminosity inferred. 



Astronomy and Cosmology 73 



Representative 
points of 
almost all 
stars are in 
this band 




2/3 1 1.5 2.25 3.38 5.0S 
Mass of star / mass of sun 

Fig. 3 The mass-luminosity diagram. 

number and accuracy than those represented in the color-luminosity 
diagram, it emerges that the luminosity of a star is closely related to 
its mass and increases rapidly with it. If one star has twice the mass of 
another star then the first star will be about 20 times as bright as the 
second. The range of stellar masses is accordingly very much smaller 
than the range in luminosity. Very few, if any, stars differ in mass 
from the sun by a factor of more than ten. 

4. These results have been described in some detail because they 
raise a series of interesting questions for the invesigator. If he wishes 
to develop a scientific theory of the internal constitution of the stars 
he must be clear about his aim. What are the observations and ex- 
periments that it should be the prime purpose of the theory to cor- 
relate? What evidence is he to regard as confirmatory and what will 
he be prepared to accept as an empirical disproof of his theory? What 
is he to regard as a satisfactory starting point for his theory? 

It should be pointed out here that the aim of science is generally 
held to be to correlate phenomena and not to explain them. A per- 
sonal judgment is required on whether an explanation is satisfactory, 
whereas the establishment of a correlation is an objective achieve- 
ment. 



74 What Is Science? 

The first step in any theory must be an examination of the guid- 
ance to be expected from terrestrial physics, which has already been 
used extensively in deriving the data to be interpreted. Thus the 
rectilinear propagation of light, the weakening of intensity with 
distance, the validity of spectroscopic inferences and the law of gravi- 
tation have all been assumed to apply. The best justification for this 
is the construction of a self-consistent theory in satisfactory agree- 
ment with observation based on such inferences and on other physi- 
cal considerations. But what guidance can physics give since the 
temperatures and pressures that must be encountered in any theory 
of stellar structure are far greater than any encountered in laboratory 
experiments? Fortunately there are good reasons for expecting cer- 
tain experimentally established physical laws to hold in stellar condi- 
tions. High temperatures and pressures imply only an assembly of 
fast atoms. Though it is impossible to experiment with dense as- 
semblies of atoms with speeds corresponding to stellar conditions, 
tenuous beams of such fast atoms can easily be produced in the 
laboratory. In fact the electrons in the beam of a television tube have 
about the same energy as the particles have, on an average, in the 
centers of the stars. The beam is, however, so tenuous that the pres- 
sure it exerts on the glass face of the screen is wholly negligible. 
While beams of much higher energies (and containing protons and 
ions as well as electrons) can be produced in specialized equipment, 
the number of particles in the beam is always too small to produce 
appreciable pressures. Nevertheless, such experiments allow us to in- 
fer the properties of hot dense assemblies. Also, gravitational fields are 
believed to be fully described by our theories up to intensities well in 
excess of stellar ones. Since conditions in stellar interiors differ greatly 
from laboratory conditions, it is possible that processes insignificant 
(and undiscovered) in the laboratory are important in stars. How- 
ever, as has been shown, this does not seem likely. The extrapolation 
of laboratory results to stellar conditions does not lead to any incon- 
sistencies or internal contradictions such as might occur in the 
mathematical extension of physical rules beyond the range in which 
they have been established. 

The dual aim of the theory of stellar structure is to correlate astro- 
nomical measurements among themselves and also, more ambi- 



Astronomy and Cosmology 75 

tiously, with physics. If terrestrial physics applied to the astronomical 
scale leads to significant results (i.e., of relevance to observations) 
then such a correlation has been achieved. Of course this may turn 
out to be impossible, but unless we start with the assumption that 
such a correlation is indeed possible we have no hope of finding it. 

5. The next step is to make a hypothetical examination of the 
properties of the matter composing the stars. In other words, assum- 
ing the law of gravitation applies, as well as other laws pertaining to 
terrestrial matter, what is the simplest model we can construct which 
will account for the observed properties of stellar bodies? Among the 
problems and questions which have to be considered are these: 

a. Is the nature of the constituent material in fact significant for 
our purposes? If the answer is yes, we must try to discover what 
stars are made of and whether a given star is composed of the 
same material throughout or varies in content from place to 
place in its interior. 

b. Are stars in a steady state or are they changing? Even a star that 
to us appears quite steady may be undergoing slow changes 
that profoundly affect its present observable properties. 

c. What other factors, besides observed properties, bear upon the 
validity of the model? Obviously if deductions from a given 
theory should deny the existence of stars possessing prop- 
erties such as are actually observed, the theory is false. But if 
according to the theory, the range of possible stellar propertied 
is wider than what is in fact observed, it may be that the theory 
is incomplete rather than false. For it may be that, although 
such stars can exist, they cannot be born. That is to say the 
limitation might lie in the process of formation rather than in 
the state of existence. To give an example from another subject, 
the strength of rocks would make the existence of mountains 
100,000 feet high perfectly possible; however, the conditions 
permitting of their formation did not occur. We can see there- 
fore at the outset that the theory of stellar constitution is closely 
linked with the problems of star formation and evolution. 



76 What Is Science? 

The simplest theoretical model satisfying our requirements incor- 
porates the following assumptions: 

(i) The material is the same throughout a star and consists 
mainly of the most abundant of all elements, hydrogen. 

(ii) Stellar bodies are in a steady state. 

(iii) Bodies so constituted, possessing such properties and ranging 
over all masses found in stars, are capable of being formed. 

These assumptions are specific enough to permit of a mathematical 
analysis of the problem. The solution is gratifying; for it turns out 
that the hypothetical bodies of the model have properties identical 
(within the limits of observational accuracy) with those of main 
sequence stars, both as regards dependence of color on luminosity 
and of luminosity on mass. 

It is most fortunate and encouraging that the simplest theoretical 
model reproduces the observable properties of the large majority of 
stars. There was a priori little reason for supposing this would be the 
case but the supporting evidence is most convincing. 

6. The method of constructing a theoretical stellar model is straight- 
forward in principle, though the details are mathematically and physi- 
cally highly complex. The gravitational forces in a star are very large 
but matter is kept from falling in by a steep pressure gradient, high 
at the center and diminishing outward. This is analogous to the 
earth's atmosphere, where the higher pressure at the bottom and the 
lower pressure on top keep the air static in spite of gravity. The 
pressure, density, and temperature of stellar matter are related in the 
same way as in a terrestrial gas 3 although the density (at the huge 
pressures) may be 100 times as great as that of water. The applica- 
bility of the gas law to this range of densities and pressures is a re- 
markable extrapolation from laboratory experiments on gases, but as 
explained earlier is well established thanks to the understanding of 
the behavior of fast particles gained by other laboratory methods. 

The temperature follows the pressure in decreasing outward from 
the center. In a star, as elsewhere, heat flows from the hotter to the 

'The pressure is the product of temperature and density multiplied by a constant 
depending only on the masses of the particles composing the gas. 



Astronomy and Cosmology 77 

colder region. This stream of heat keeps the surface of the star hot, 
although the glowing surface constantly radiates into space. The in- 
ternal temperature gradient leads to a flow of energy from the in- 
terior to the surface. The light radiated by the star is the external 
continuation of the internal energy flow. The magnitude of the 
temperature gradient just below the surface is hence essentially deter- 
mined by the rate of radiation per unit surface area and so by the 
surface temperature, while the pressure gradient affords support 
against gravity and accordingly depends on the mass and radius of 
the star. The properties of the internal heat flow, together with the 
gas laws and the pressure support against gravity, imply that there 
must be a certain relation between the mass, luminosity and radius 
of any simple homogeneous star, a relation that can be shown to hold 
for observed stars of the main sequence. 

How is the heat flow maintained, i.e., where does the energy come 
from? Consideration of the period for which the heat flow has been 
maintained helps to answer this question. 

Geological evidence indicates that the sun's luminosity has not 
changed appreciably for several hundreds of millions of years, and 
less direct arguments indicate that the sun, as well as many other 
stars, are several billion years old. No chemical or gravitational source 
of energy could sustain the required rate of burning for so long a 
period. Nuclear energies alone can account for the phenomenon. 
Nuclear energy is released in two processes, spontaneous radioactivity 
and induced transmutation. In the first, a suitable nucleus emits a 
particle and turns into a different nucleus owing to the play of in- 
ternal forces. Spontaneous radioactivity cannot be the source of stel- 
lar energy because radioactive materials are rare and because they 
liberate relatively little energy. Induced transmutations occur when 
a nucleus is hit by another particle, the collision being so hard that a 
nuclear reaction results. Some of these reactions consume part of the 
energy of the incident particle; others release energy. There are two 
chief methods for producing sufficiently hard collisions. In the labora- 
tory, fast beams of particles are produced and directed at suitable 
substances. It seems most unlikely that anything corresponding to aa 
apparatus for producing fast beams can be found inside the stars. In 
the second method, material is heated to a high temperature so that 



78 What Is Science? 

the constituent particles move at high speed. Nuclei may then collide 
sufficiently fast to lead to nuclear transmutations. A reaction of this 
type is called thermonuclear and is evidently a possible energy source 
for the stars, if the heat produced in the nuclear reactions keeps the 
material so hot that the reaction continues. 

To arrive at more definite conclusions, numerical values have to be 
considered. The temperature at the centers of the stars can be in- 
ferred from heat flow arguments and observed characteristics of the 
stars to be around fifteen million degrees centigrade. The average 
velocity of nuclei at such temperatures is very low by laboratory 
standards. The velocity of nuclei in beams required to produce a 
measurable rate of nuclear transmutations is considerably higher. But 
this discrepancy is only apparent. The rate of energy production per 
unit mass in stars is exceedingly low by terrestrial standards. Thus 
200 pounds of material at the center of the sun produce merely one 
watt; whereas, for example, the average heat output of a human being 
is around 100 watts. The enormous luminosity of the stars is there- 
fore due only to their tremendous masses. To put it more precisely, 
consider a thin cone with its vertex at the center of the sun and its 
base an area of one square inch of solar surface. Though energy is 
produced only at the exceedingly low rate mentioned above along 
the part of the cone near the vertex, the enormous size of this region 
(say 70,000 miles long) and the high density of the matter (several 
times as dense as lead) imply that the total output of energy is quite 
large. All this energy has to flow out through one square inch of 
surface area, since, by symmetry, there is no net outflow to neigh- 
boring cones. Hence the surface is kept hot and the whole star is 
bright. 

Due account being taken of this factor, laboratory experiments 
can be performed in nuclear physics to determine the central tem- 
perature at which suitable thermonuclear reactions (in fact the 
conversion of hydrogen into helium), proceeding at a sufficient rate, 
produce the total heat output of stars. Knowledge of the central 
temperature in turn affords understanding of a relation between 
mass, radius and luminosity in addition to the one referred to above, 
and, like it, in excellent agreement with the observed characteris- 
tics of main sequence stars. Thus we have arrived at the conclusion 



Astronomy and Cosmology 79 

that a homogeneous mass (of stellar magnitude) consisting princi- 
pally of hydrogen can be inferred from ordinary physics to be in 
equilibrium when its surface temperature and luminosity have cer- 
tain values, and these are the observed values for a normal star of the 
same mass. 

This is an impressive vindication of the scientist's method of not 
ascribing processes in unfamiliar settings to "mysterious forces un- 
known to science," of not meekly saying "I do not know/' but of 
resolutely applying the known and extending it to cover the un- 
known. 

7. Since the homogeneous models consisting of matter behaving as 
a gas and composed chiefly of hydrogen reproduce the observable 
properties of main sequence stars, we are encouraged to devise 
models to match the other, rarer, types of stars. 

It has been pointed out that the high temperatures of normal 
stellar interiors justify the astrophysicist in regarding matter existing 
there as being in a gaseous state despite its high density. At con- 
siderably higher densities than are met in main sequence stars new 
factors come into play. The famous exclusion principle of atomic 
physics formulated by the Nobel-prize winning Swiss scientist, Wolf- 
gang Pauli, states that no two electrons can be close to each other 
both in position and in velocity. In highly compressed matter numer- 
ous electrons are close to each other in position. Accordingly numer- 
ous sufficiently different velocities must occur. This implies that many 
electrons must have a high speed. At ordinary densities, the velocity 
of particles depends only on the temperature, but the exclusion prin- 
ciple implies that in highly compressed matter the velocity of many 
particles must be high whatever the temperature. 

The impact of fast particles is the pressure; accordingly highly 
compressed matter exerts considerable pressure irrespective of the 
temperature. This type of pressure therefore follows different laws 
from the usual gas pressure. Models can be examined in which this 
peculiar pressure affords the main support against gravitation. It turns 
out that the radius is a definite function of the mass, that the mass 
must be below a certain limit, but that the luminosity is indetermi- 
nate. Though points of comparison with observation are far fewer than 



80 What Is Science? 

in the case of main sequence stars, the model seems to be in excellent 
agreement with all that is known of white dwarf stars. 

According to the model that corresponds to the main sequence 
stars, their energy is provided by the thermonuclear conversion of 
hydrogen into helium in the central regions. After a sufficient lapse 
of time such a star will have produced a great deal of helium, and 
hydrogen will no longer be the principal constituent. If the helium 
stays near the center where it has been generated, the inner regions 
will have a different composition (large proportion of helium) from 
the outer ones (almost pure hydrogen). The star will cease to be 
homogeneous. The time needed to bring about such changes can 
easily be computed. The rate of transmutation which will account for 
the star's luminosity follows from the known amount of energy liber- 
ated in each nuclear reaction. The mass of hydrogen turned into 
helium in, say, a billion years is simply proportional to the star's 
luminosity. As this in turn is such a steeply increasing function of the 
star's mass, it follows that a far larger fraction of the mass of a mas- 
sive (and hence bright) star will be helium after a billion years than 
in the case of a light (and hence faint) star. The hydrogen store of 
the sun would last for about one hundred billion years, so that signif- 
icant changes in appearance might be expected after about ten billion 
years. For fainter stars this period is much longer, for brighter ones 
much shorter. Since no star in our galaxy is believed to be more 
than 5-10 billion years old, no star fainter than the sun can have 
accumulated much helium, but stars brighter than the sun may well 
have done so. Though many uncertainties are involved, it seems clear 
that a star with large amounts of helium in the inner regions is likely 
to be greatly expanded and hence to look much redder than a normal 
star. Thus we seem to have found, in principle at least, satisfactory 
models for red giant and supergiant stars. 

A particularly successful feature of this theory is the fact that it 
implies that stars fainter than the sun should be confined to the main 
sequence while brighter stars may be found to the right of it. This 
agrees perfectly with the Hertzsprung-Russell diagram. 

Nevertheless it must not be supposed that we are within striking 
distance of having theoretical models for all stars. The luminosity of 
some stars varies periodically, a fact which may indicate that they 



Astronomy and Cosmology 81 

oscillate. The magnetic field of stars can sometimes be found by its 
effect on the spectrum. It turns out that certain stars have high, and 
some variable, magnetic fields. Also some stars have a rather lower 
luminosity than main sequence stars of the same color. These so- 
called sub-dwarfs do not fit in too well with the interpretation of the 
Hertzsprung-Russell diagram given above. Though we are slowly 
gaining in understanding of these stars, no wholly satisfactory theory 
of their behavior exists. The success of the theory in describing nor- 
mal stars gives one, however, great confidence that it will eventually 
also be able to describe the rarer types without having to rely on 
other than known properties of matter. 

8. So far the discussion has been largely confined to stars in our 
astronomical neighborhood. Are they representative of stars every- 
where? This question leads directly to the organization of stars into 
galaxies. 

The Milky Way is a familiar phenomenon of the night sky. It is 
an arrangement of vast numbers of stars in a flattened disk-shaped 
portion of space. The solar system is close to the plane of the disk, 
though fairly distant from its center (about 25,000 light years, while 
the radius of the disk is about 40,000 light years). If we look around 
us in the plane of the disk we see large numbers of stars, while in any 
other direction we look out of the disk and hence see far fewer stars. 
This explains the luminous arc of the Milky Way. 

Our galaxy is not embedded in empty space, but is surrounded, 
though at great distances, by innumerable similar galaxies. The best 
known of these is the great Andromeda nebula, visible to the naked 
eye. A great many more galaxies are accessible to a large telescope. 
Many prominent galaxies show a spiral structure, i.e., the bright stars 
are arranged in spiral arms, with less luminous regions between them 
(Fig. 4). Intricate detailed investigations have shown that the stellar 
population in the spiral arms resembles that of the solar neighbor- 
hood but differs from stellar populations elsewhere. In particular it is 
important to point out that while stars redder than main sequence 
stars are found outside the spiral arms, they are not as red as the 
spiral arm "red giants/' and also that hot blue stars are confined to 
the spiral arms. 



82 What Is Science? 




Fig. 4a A spiral galaxy-a nebula in Ursa Major (from a Mt. Palomar 

photo). 




Fig. 4b A spiral galaxy seen edge on-a nebula in Coma Berenices (from 
a Mt. Palomar photo). 

Because of our location we are unable to see our own galaxy from 
the outside; but various observational data, including star counts in 
different directions, measurements of stellar velocities and of occur- 
rence of bright stars and star clusters, show convincingly that ours is a 
spiral galaxy, and that we are situated in a spiral arm. 



Astronomy and Cosmology 83 

Why do different types of stars exist in different parts of a spiral 
galaxy? The appearance of the Milky Way is distinctly patchy, and 
there are some very black regions, among them the well-known "Coal 
Sack." In view of the inherent improbability of a long vacant corridor 
amidst millions of stars, it has long been thought that this blackness 
is not due to paucity of stars, but to the presence of obscuring mat- 
ter, i.e., of material tenuous by terrestrial standards, yet as opaque as 
smoke or fog owing to its disposition in the form of huge clouds. By 
examining the light of stars not wholly blacked out, but partially 
dimmed, the properties of the intervening medium can to some ex- 
tent be established. It consists of small, solid particles of ice, carbon, 
calcium compounds, and the like, and so is referred to as dust. The 
discovery of the existence of this nonluminous matter caused a revo- 
lution in astronomy, which until then had been concerned exclusively 
with the shining stars, supposedly the only inhabitants of space. How- 
ever, even more startling discoveries were to come. Certain arguments, 
partly dynamical and partly spectroscopic, indicated that besides the 
dust, there was also cold gas (mainly hydrogen) in the space between 
the stars, in quantity greatly exceeding the dust, and probably not 
less than the stellar matter. The interstellar gas is so tenuous that 
there are at most a thousand of its atoms in a cubic centimeter; a 
volume of this gas equal to that of the earth would have a mass of 
only one ton. However, the regions filled with interstellar gas are so 
large that huge masses exist and have a strong influence on the evolu- 
tion of the stars. 

Because the atoms of the gas move at the relatively low velocity of 
one kilometer per second it is said to be cold. It is optically inactive 
in that it neither shines nor absorbs light from stars behind it. How- 
ever, collisions between the gas atoms are sufficient to result indi- 
rectly in the production of radio waves and they have been detected 
in quite recent investigations. Not only have these radio observations 
confirmed the inference that the gas exists, but they are also helping 
to establish the distribution of the gas clouds and so render more 
accurate our knowledge of the spiral structure of our galaxy. 

The gas clouds and particularly the dust clouds seem to be con- 
centrated in the spiral arms. The special character of the stars in the 
spiral arms is therefore supposed to be due to their interaction with 



84 What Is Science? 

the local accumulation of gas and dust. What is the nature of this 
interaction? This is one of the most absorbing fields of present-day 
research. It is partly concerned with the problem of the origin of the 
stars, of their supposed birth in such clouds. Another aspect of the 
problem is the increase in the mass of a star which results if it strongly 
attracts the material of a cloud and causes the gas to fall into the 
star. Thirdly, there is the opposite process, in which some stars 
(probably very few, but possibly many) replenish the dust clouds by 
sloughing matter from their surfaces. 

The subject is too involved to be discussed in detail, but it will be 
seen that there are fascinating problems: the relation between the 
character of a star and its position in the galaxy, the origin of the 
stars, the maintenance of the very bright stars that so quickly exhaust 
their hydrogen, and kindred matters. 

9. To the nonscientist it must seem strange that, while the history 
of science appears to be a brilliant success story, from a logical point 
of view the stress is always on disproof and hence on the failure 
rather than on the confirmation of theories. There are many con- 
tributory reasons for this apparent discrepancy between the workshop 
procedure and the nature of the finished product. The most obvious 
of these reasons is that in describing the present state of any more or 
less complete subject one refers only to the theory that has survived 
and not to those that have been disproved. 

The less complete a science, the more evident is the ruling part 
played by empirical disproof in its development. Cosmology is a case 
in point; and the essentially primitive state of this science facilitates 
the examination of its methods of inference and analysis. 

The subject matter of cosmology is the structure of the universe as 
a whole. For a long time it was believed (and some persons still cling 
to this view) that, because of its subject matter, cosmology belonged 
to philosophy rather than to science. It was only 130 years ago that a 
pioneer investigation by the German astronomer Heinrich Olbers 
demonstrated the scientific character of cosmology. This investiga- 
tion remains one of the most important arguments in cosmology and 
so it will now be considered in some detail. 

Near stars, which appear on the average to be bright, are few in 



Astronomy and Cosmology 85 

number. Medium-bright stars are more common, faint ones com- 
moner still. It is known that there are stars too faint to be individ- 
ually visible. The question is: are they so numerous that the diffuse 
background light received from them is significant? It is evident that 
in order to calculate effects emanating from distant regions of un- 
resolvable stars, assumptions have to be made about the nature of 
these regions. One may then attempt to infer the intensity of the 
background light of the sky and compare this with observational ex- 
perience. 
The investigation proceeds in three stages: 

a. A set of assumptions is formulated whose fruitfulness and plausi- 
bility is tested in stages (b) and (c). These assumptions need not 
(and generally will not) be susceptible to direct observational check. 

b. Observable consequences are deduced from the assumptions. 

c. The empirical connection is established by comparing the conse- 
quences of the assumptions with the actual observations. If there is 
disagreement, then (a) has been disproved. If there is no disagree- 
ment, then (a) remains tenable pending the exploration of further 
observable consequences. A set of assumptions that does not lend 
itself to (c) and hence cannot be disproved is empty and scientifi- 
cally futile. 

Olbers made the following four assumptions about the nature of 
distant regions: 

(i) Viewed on a sufficiently large scale, the universe is the same 

everywhere, i.e., it is uniform in space, 
(ii) Similarly, it is unchanging in time. 4 
(iii) There arc no major systematic motions, 
(iv) The laws of physics, as we know them, apply everywhere 

throughout the universe. 

Some comments on these assumptions may be appropriate. As for 
(i), it will be required that for sufficiently large regions the amount 
of light emitted by stars per unit volume shall be the same for each 
region. The known aggregation of stars into widely separated galaxies 
does not upset this assumption; it merely compels the fixing of 

4 Assumption (i) is known as the cosmological principle, assumptions (i) and (ii) 
together as the perfect cosmological principle. 



86 



What Is Science? 



boundaries large enough so that each region will include many gal- 
axies. 

Assumption (iii) means that while individual stars or galaxies may 
have randomly distributed velocities, small compared with the veloc- 
ity of light, they are not correlated with position. In particular the 
assumption denies the possibility that distant galaxies recede from 
us systematically. The main consequence of the assumption is that all 
effects of velocities are held to be negligible. 

Assumption (iv) is almost indispensable, at least as a starting point, 
for without it we should have to discard all the knowledge discovered 
in our neighborhood and would scarcely be able to proceed. 

Consider now a set of spheres, each centered on us, the difference 
between the radii of successive spheres being a constant length 
which will be taken to be large. Any two adjacent spheres enclose a 
spherical shell between them, and if the radii of the spheres are very 
large compared with their difference in length, the ratio of the dis- 
tances from us of any two points inside a shell must be close to unity 
(Fig. 5) . It will now be assumed that the volume of each of the shells 



Star 




Fig. 5 Gibers' paradox. Four of the evenly spaced concentric shells are 
shown. Observe that all stars in any one shell are approximately equidistant 
from us, and also that the light from a star in a shell has spread, w/icri it 
reaches us, over a sphere of about the same size as the boundary spheres 

of the stars shell. 



Astronomy and Cosmology 8? 

to be considered is so large that assumption (i) applies. The numbet 
of stars in any shell, and hence their total rate of emission of light, is 
accordingly proportional to the volume of the shell. Since the thick- 
ness of each shell is the same, its volume is, with fair precision, pro* 
portional to the surface area of the inner (or equally the outer) 
boundary sphere of the shell. 

What of the light sent out by a star in the shell? By the time the 
light reaches earth it will have spread over a sphere whose radius is; 
the distance from the star to us. If the thickness of the shell is disre-- 
garded a permissible procedure, as has been indicated it follows 
that this distance is in effect equal to the radius of either boundary 
sphere. The intensity of light received from any one star is therefore 
inversely proportional to the surface area of (either) boundary sphere 
of the shell in which the star is situated. Since the number of stars is 
directly proportional to this quantity, the total intensity of light re- 
ceived from all the stars in a shell is independent of the radius of the 
shell and hence the same for all shells. In other words the amount of 
light contributed by distant shells is the same as the amount due to 
near shells because the increase in the number of stars offsets th 
diminution in the brightness of each star. 

Since each shell contributes the same amount of light, and by 
virtue of Gibers' assumptions the shells continue without end, it is 
hard to understand why we are not drowned in an infinite flood of 
light emanating mainly from extremely distant, very faint, but im* 
mensely numerous stars. The fallacy in this reasoning is that no al* 
lowance has been made for the fact that each star not only sends out 
light, but also intercepts (owing to its finite size) light from yet more 
distant stars. Because of the relatively small size of stars, this shadow- 
ing effect becomes important only at very large distances. When al- 
lowance is made for it, the intensity of light turns out to be finite, 
but as great as on the surface of an average star. This is equal to 
about 40,000 times the intensity of sunlight on the earth when the 
sun is in the zenith. It is worth remarking that this result, which 
may be called Gibers' paradox, can also be reached by another train 
of reasoning. According to the assumptions we have adopted, if one 
looks into the sky in any direction the line of sight will eventually 
intercept a stellar surface. Since this means that we are in a sensQ 



88 What Is Science? 

entirely surrounded by stellar surfaces, the identical paradox follows. 

But this conclusion is so completely refuted by the fact that it is 
dark at night, that the assumptions must obviously be incorrect. 5 
This is a most important result, for a set of assumptions about the 
nature of the universe has been disproved empirically. We know as a 
result of observation that whatever the depths of the universe may be 
like, they do not conform to the model based on Gibers' assump- 
tions. With this step the relevance and supremacy of observational 
disproof has been established in cosmology and it has become a sci- 
ence. 

The next step is to tinker with the set of assumptions, to see what 
can be saved, what must be substituted or mended. We have agreed 
that it is unwise to tamper with assumption (iv) (laws of physics) 
unless there are compelling reasons to do so. Also there is strong 
observational evidence in support of assumption (i) (uniformity of 
the universe), as will be shown below. Can Olbers' paradox be 
.avoided if either (ii) (unchanging nature of the universe) or (iii) 
(no motion) is dropped? 

In the case of (ii), it is easy to see that if the stars began to shine 
not too long ago, the paradox does not arise. For since light has a 
finite velocity, the light from the remote shells must have been 
emitted in the very distant past to arrive here now. If at that time 
no light was in fact emitted, then shells beyond a certain distance 
will not contribute to the present intensity of the background light 
of the sky, and so agreement with observation may be reached. 

In the case of (iii) a certain amount of mathematical work has 

* It is useless to suggest, as Olbers did, that dust clouds absorb the light from dis- 
tant regions. For in doing so the clouds would get hotter until they glowed strongly 
enough to emit as much as they received. By assumption (ii) there has been ample 
time for this state to be reached, in which there is no resultant shielding by ab- 
sorbing matter. It should also be noticed that Olbers' paradox is unaffected by the 
much discussed possibility that the geometry of large-scale regions differs from 
local (Euclidean) geometry in such a way that the universe is finite. By assump- 
tion (i) a finite universe would be unbounded, so that light could travel around 
it arbitrarily often, just as one can circle the globe arbitrarily often. Accordingly 
we would not only receive light from a star directly but also light it has emitted 
that has circled the globe once, twice, and so on. Therefore in this model a finite 
number of stars produces an infinite number of star images; thus the paradox re- 
>main$ unresolved. 



Astronomy and Cosmology 89 

to be done to see what types of motion are at all compatible with 
(i). It turns out that the only systematic motions compatible with 
uniformity are those in which relative to any particular member (gal- 
axy) every other member is moving, in the line of sight, with a 
velocity proportional (roughly speaking) to its distance. Either the 
whole system is expanding or it is contracting. Now it is known from 
ordinary physics that light from a receding source appears dimmer 
than light from a similar stationary source, that this effect becomes 
very pronounced when the velocity of the source is close to the 
velocity of light, and that the opposite holds (increased brightness) 
if the source is approaching. Accordingly, in an expanding system the 
distant regions contribute less than in a stationary system to the back- 
ground light of the sky, and hence Gibers' paradox does not arise in 
such an "expanding universe" provided the increase of recession ve- 
locity with distance is sufficiently rapid. In a contracting system the 
paradox would correspondingly be enhanced. 

There are thus two ways of resolving Gibers' paradox while main- 
taining assumptions (i) and (iv). Either the system is young in that 
the stars only began to shine a finite time ago, or any two galaxies 
recede from each other with a velocity proportional to their distance 
apart. 

There are several important cross links between theory and ob- 
servation at this stage. The light from faint and hence presumably 
distant galaxies shows precisely the observable characteristics asso- 
ciated with light emitted by receding sources. The velocities inferred 
from these characteristics turn out to be proportional to the distance, 
which in turn is inferred from the apparent faintness. The greatest 
velocity so inferred is almost 40,000 miles per second, a fifth of the 
velocity of light, and the faintest galaxies visible in the biggest tele- 
scope are presumably considerably faster. 

These facts lend support to one of the suggestions above for avoid- 
ing Gibers' paradox. Second, the fact that the observed motion is 
identical with the only pattern (velocity proportional to distance) 
compatible with the assumption of uniformity confers even greater 
plausibility on this assumption than does the observed degree of uni- 
formity in the distribution of galaxies. Finally, a more recondite re- 
mark may be permitted. It could be argued that the observations of 



90 What Is Science? 

uniformity and motion refer to a negligibly small part of the entire 
universe, and therefore assumption (i) is inadequately corroborated. 
This argument, however, rests upon an incorrect notion of the mean- 
ing of the word "universe." Cosmology is a science and as such only 
concerned with observables. The validity of Gibers' assumptions for 
regions beyond the limit of observability is wholly irrelevant, even if 
such regions can be said to exist. The question deserving attention is 
whether the observed region forms a sufficiently large fraction of the 
observable region to allow inferences to be drawn in a plausible 
manner. 

A shadowy and pragmatic boundary of the observable universe is 
suggested by the dimming associated with the velocity of recession. 
For this dimming proceeds so rapidly with increasing distance that 
regions beyond a certain range are effectively unobservable. In fact 
the latest doubling of telescope aperture has not doubled the accessi- 
ble distance, but increased it only by a markedly smaller fraction. 
At still greater distances the law of diminishing returns would operate 
more strongly so that a doubling of telescope aperture would only 
increase the observable distance by a few per cent or even less. Al- 
though there may not be an absolute bar to seeing arbitrarily far, 
an elastic but nevertheless effective limit is imposed by the recession 
velocity. The highest recession velocity measured is about a fifth 
of the velocity of light and some faint galaxies observed may have a 
velocity of recession close to one-third of the velocity of light. There 
is every reason to believe (by virtue of the theory of relativity) that 
if an object recedes so fast as to be almost invisible, all other types of 
interaction will also be insignificant. Though no exact definition of 
effective observability has yet been given, we must nevertheless con- 
clude that our observations cover an appreciable part of the effec- 
tively observable region. Accordingly they can be said to give sub- 
stantial support to the validity of assumption (i) (uniformity) with 
respect to the regions that are scientifically relevant. 

10. To make a further advance, one must construct a comprehen- 
sive theory of cosmology that attempts to connect observations with 
each other and with the rest of physics. In view of the scarcity of 



Astronomy and Cosmology 91 

available data it is not surprising that there are several theories which 
can be fitted to present observations. Among these theories there are 
two that seem to be most promising and have attracted most at- 
tention. They alone will be discussed in this essay. 

Before entering upon a detailed description of these two theories 
and their differences it may be helpful to summarize the points com- 
mon to them. These are: 

a. The assumption of the spatial uniformity of the universe 
(Gibers' assumption (i) ) known as the cosmological principle. 
It is agreed that this assumption can only apply on a very large 
scale, since on any moderate or small scale the universe is far 
from uniform as shown by the existence of galaxies and stars. 
The evidence for the cosmological principle has been discussed 
above. 

b. The recession of the galaxies, also known as "the expansion of 
the universe/' The evidence for this is the so-called red shift 
of the spectra of the galaxies referred to before. The only known 
interpretation of such an ^servational effect is a velocity of 
recession. Though the notion of the expanding universe seems 
to have caused some difficulty of understanding, few scientists 
are willing to postulate a special hypothetical effect to account 
for the red shift. The two theories to be discussed both accept 
the obvious interpretation of the red shift as due to a velocity of 
recession and hence as clear-cut and sufficient evidence for the 
expansion of the universe. 

The difference between the two theories arises from the attitude 
they adopt towards Gibers' assumption (ii). The so-called steady- 
state theory accepts this assumption of the unchanging appearance 
of the universe and considers the pair of assumptions (i) and (ii) 
(also known as the perfect cosmological principle) as fundamental. 
Even assumption (iv) (the applicability of the laws of physics) is 
regarded as secondary compared with the perfect cosmological prin- 
ciple. In the other theory assumption (ii) is dropped, assumption 
(iv) being considered as the basis of the theory. Since the formula- 



92 What Is Science? 

tion which has been adopted of the behavior of matter in the large 
is general relativity, this cosmological theory is known as relativistic 
cosmology. 

Taking first the steady-state theory, the chief argument in favor of 
maintaining both assumptions (i) and (ii) (the perfect cosmologi- 
cal principle) is one of necessity, based on the circumstance that our 
knowledge of physics has been gathered here on earth and in our 
astronomical neighborhood. In other words our experience is based 
on the exploration of regions minute on the cosmic scale, in a period 
of time similarly minute. There is, to be sure, no immediate reason 
to believe that the laws of physics so acquired are of universal valid- 
ity. On the contrary it can be argued forcefully that the quantities 
entering in our laws of physics that are known as physical constants 
(the constant of gravitation, the ratio of electric to gravitational 
forces in an atom, etc.) are not true constants but depend on the 
structure of the universe. If the universe varies from place to place 
or from time to time, these "constants" must vary too, but in a way 
unknown to us. It is only because our local region and the period of 
physical measurements are so small that these quantities are appar- 
ently constant. Any contemplation of a changing universe precludes 
therefore the extrapolation of local physical laws, unless a (largely 
arbitrary) assumption is made as to how they vary with this change. 
The only way to avoid this additional complexity is to assume that 
the universe does not change (on the large scale) in space or time, 
which is to adopt the perfect cosmological principle. 

Of course this step does not imply that the perfect cosmological 
principle is correct; but its fruitfulness is self-evident, since the prin- 
ciple leads without further assumptions to predictions susceptible of 
observational disproof. On the strength of this feature some, but by 
no means all, scientists working in the field accept the perfect cos- 
mological principle. The main argument for rejecting it is that it 
leads to a modification of the laws of physics that many find un- 
palatable. The need for this modification follows directly from the 
discussion of the preceding section. It was shown that the only plausi- 
ble resolutions of Olbers' paradox are either to substitute for (ii) the 
assumption that the universe is young or for (iii) the assumption 



Astronomy and Cosmology 93 

that it is expanding. 6 Either choice has drastic implications. The first 
contradicts the perfect cosmological principle. The second, which 
leaves the principle intact, can be fitted into the framework of the 
steady-state theory, expansion being inferred from the darkness of the 
night sky and other more direct observations. But if this course is 
followed a fundamental law of physics must be revised. For the ex- 
pansion seems to imply, in the light of the law of conservation of 
mass, a diminishing average density of matter. As this flatly contra- 
dicts assumption (ii) of the unchanging character of the universe, the 
only way to preserve the perfect cosmological principle is to modify 
the law of conservation by permitting a continual creation of matter. 7 
The rate of creation must be such as to cancel the diminution in 
density due to the expansion of the system. It can further be shown 
that, in order to maintain the unchanging character of the universe, 
creation must proceed at a fairly uniform rate, that is to say, the rate 
per unit volume per unit time must be constant regardless of the 
presence or absence of matter or radiation. The matter created must 
be cold diffuse hydrogen or its equivalent. 

The process rate comes to about one atom of hydrogen per cubic 
foot every few billion years. It is evident that this yield is much too 
small to be detected. But it is also important to realize that the ex- 
periments on which the law of conservation of matter are based are 
too crude by factors of hundreds of billions to exclude the possibility 
that matter is being created at this slow rate. Thus no contradiction 
confronts us between the continual creation theory and observational 
fact, though the theory certainly does not jibe with current mathe- 
matical formulations. It is this formal disagreement which leads 
many scientists to prefer a different theory. 

The view favored by many is based on the theory of relativity, 



If assumption (i) is eliminated the difficulty of the background light can be 
quite simply resolved by assuming that beyond a certain distance there are no 
stars. However, the arguments in favor of assumption (i) are so strong that it 
cannot be dropped. 

7 The chain of arguments used is: perfect cosmological principle plus dark night 
sky implies expansion; perfect cosmological principle plus expansion implies con- 
tinual creation. 



94 What Is Science? 

whose formulation of the laws of the behavior of matter in our 
neighborhood agrees most closely with observation Relativity in- 
corporates the law of conservation of mass and is therefore, in its 
usual interpretation, incompatible with the perfect cosmological prin- 
ciple owing to the expansion of the universe. Assumption (i) (uni- 
formity) is compatible with general relativity. The expansion of the 
universe is not only directly inferred from observation but is to some 
extent implied by the theory. The combination of uniformity, ex- 
pansion and general relativity leads to a homogeneous, changing, 
and evolving universe. At any instant there is large-scale uniformity 
and changes are taking place everywhere in such a manner that all 
regions keep in step and so maintain the uniformity of the system. 
The assumption is made that in spite of the changing character of 
the universe the laws of general relativity apply at all times. 

Of the several different models compatible with this set of ideas, 
cosmologists studied most the model invented by the noted Belgian 
physicist, the Abb Lemaitre, and elaborated by the American, George 
Gamow. Its main features are the following: at the beginning the 
universe was in an exceedingly hot and dense state; there ensued a 
nuclear type of explosion in which the heavy elements were formed. 
In the early phase of rapid expansion following the explosion, mat- 
ter was uniformly distributed without local agglomerations such as 
stars and galaxies. Under the influence of gravitation the expansion 
slowed down almost to a standstill. During this nearly static period 
the condensation of galaxies took place. After a time a repulsive 
force the concept fits naturally into relativity began to counter- 
balance gravity and expansion resumed. At present the universe is 
in an advanced stage of the second period of expansion, which 
continues at an increasing pace. The resulting diminution of density 
has made impossible the condensation of new galaxies. 

Lemaitre's universe is therefore evolving, starting with a violent 
birth and continuing through distinctive periods of aging. His model, 
like that based on the perfect cosmological principle, leads to a 
coherent description of the universe in agreement with what is 
known. However a number of observations that can be made now or 
in the very near future will furnish results which are forecast differ- 
ently by the two theories and will therefore invalidate one or the 



Astronomy and Cosmology 95 

other. Thus each is susceptible of disproof and both qualify as proper 
scientific theories. 

One of the crucial results turns on the basic characteristics of the 
two theories. In the steady-state model based on the perfect cosmo- 
logical principle the unchanging character of the entire universe is 
maintained, in spite of the aging of each individual galaxy (mainly 
due to the conversion of hydrogen into helium in the stars ) , by the 
continual formation of new galaxies from newly created matter in the 
constantly increasing spaces between the old ones. On the other hand 
as a galaxy grows old it drifts away into less and less observable re- 
gions through the process of expansion. In this way a population 
equilibrium is maintained just as in a stationary human population, 
where deaths are balanced by births and, though each member ages, 
the average of the population is constant. This model therefore ex- 
hibits galaxies of widely different ages everywhere and at all times, 
but in any region containing large numbers of galaxies the average 
age is always the same. 

A different age distribution characterizes the relativistic model. The 
underlying theory provides for periods in the evolution of the uni- 
verse favorable to the formation of galaxies, and other periods (in- 
cluding the present) with conditions unfavorable to the process. 
Accordingly all galaxies are more or less of the same age. 

The observational testing of these antithetical conclusions might 
be accomplished in two distinct ways. One involves looking at galaxies 
reasonably close to ours, estimating their age distribution and seeing 
whether it conforms to either of the theoretical forecasts. This 
method, though attractive, cannot yet be applied because present 
knowledge does not permit of an estimate of the age of a galaxy from 
its appearance; but it seems likely that this obstacle will be overcome 
during the next ten years or so. Galaxies fall into different classes 
based on their appearance. It should be possible, with the aid of the 
theories of stellar structure and evolution discussed earlier in this essay, 
to discover whether the stellar content of one type of galaxy gradually 
changes to the stellar content of some other type. This should make 
it feasible to change the present purely morphological classification 
of galaxies into an evolutionary scheme and so to correlate the ap- 
pearance of a galaxy with its age. 



96 What Is Science? 

The second method, for which the necessary observations can be 
made now, is a little harder to explain. It involves the consideration 
that, owing to the finite velocity of light, the images of distant galaxies 
seen today portray their appearance a long time ago. According to 
the perfect cosmological principle, which implies changelessness, 
the time lapse does not matter. On the average the various observable 
properties (color, shape, size) of galaxies were the same in the remote 
past as they are now, so that the properties should be the same foi 
distant as for near galaxies. But if one goes by the relativistic model, 
one must conclude that the distant galaxies are seen today in an early 
stage of their evolution and their characteristics therefore differ from 
near ones. 

This test consists then in observing whether there is a systematic 
variation with distance of the average color, size, and shape of galax- 
ies. If the variation exists, the perfect cosmological principle is un- 
tenable; the absence of variation would support the principle. Ob- 
servational work along these lines is feasible with existing equipment 
and is about to be carried out. 

This brief and compressed description of work in various fields of 
astronomy cannot claim to be comprehensive. It does however try to 
show how the whole of scientific endeavor is directed solely to ob- 
taining, correlating, and forecasting observational results. Theories 
must not only agree with the facts; they must be so constructed as to 
facilitate attempts at empirical disproof. The data so obtained and 
the standard of internal consistency are the only legitimate criteria for 
science. Intuitive reactions, such as the difficulty of imagining various 
strange and remarkable features of a theory (in astronomy and cos- 
mology, these include temperatures of millions of degrees, creation 
of matter, enormous velocities, etc.) are of secondary importance. 
The methods touched upon in this essay have proved themselves re- 
peatedly in many branches of science; they have focused issues and 
organized congeries of facts and conjectures into statements capable 
of being tested, questions capable of being answered. Cosmology, 
though an infant discipline, confronted with prodigious exercises, has 
made progress only by availing itself of these methods. It will con- 
tinue to do so. 



PHYSICS 



EDWARD U. CONDON 



about 

Edward U. Condon 



Edward U. Condon was born in 1902 in Alamogordo, New Mex 
ico. His father was a western civil engineer who specialized in building 
railroads (he put the Western Pacific through the Feather River Can 
yon) and Condon's boyhood was, therefore, spent in nearly all of the 
states west of Denver. He went to high school in Oakland, California 
and worked as a newspaper reporter from 1918 to 1921 before enter- 
ing the University of California. In 1926 he received his Ph.D. there 
and went to Germany for a year's study. This was just at the lime 
when the new quantum mechanics of Heisenberg, Born, Schrodinger 
and Dirac was being developed. On his return Condon spent a year 
at Columbia University and at the Bell Telephone Laboratories and in 
1928 joined the faculty of Princeton University. He remained there 
until 1937, except for one year spent as professor of theoretical physics 
at the University of Minnesota. During this period he de~t>eloped the 
theory of radioactive decay with the late Ronald Gurney and wrote a 
definitive treatise on the theory of atomic spectra with George H. 
Shortley. These researches established his reputation as a foremost 
theoretical physicist. 

In 1937 he was appointed Associate Director of Research for the 
Westinghouse Electric Corporation; in this post he developed a pro- 
gram of nuclear research before the discovery of uranium fission. One 
of the important advances achieved in these studies was the discovery 
by Condon's associates of the phenomenon of photo-fission, the pro- 

98 



about Edward 17. Condon 99 

duction of uranium fission by means of gamma radiation. In 
1940 Condon turned the major part of his energy to defense work, 
starting with research on microwave radar at Westinghouse and at the 
government-sponsored project at the Massachusetts Institute of Tech- 
nology. The next year he was appointed a member of the then-secret 
S-l Committee set up by President Roosevelt to plan the atomic 
bomb project. He was closely associated with the government's 
atomic bomb research for the rest of the war. 

Immediately after the war, beginning in the fall of 1945, he took 
a leading part in the campaign of the atomic scientists to acquaint the 
American public with the social and political problems raised 
by atomic energy and atomic bombs. He is responsible in no small 
measure for the success of this program, which enlightened the 
thoughtful segment of American opinion and gained administration 
support for the legislation that placed atomic energy under civilian 
rather than military control. For almost a year Condon gave valuable 
service as scientific adviser to the U.S. Senate Special Committee on 
Atomic Energy, which, in the Seventy-ninth Congress, held extensive 
hearings, and voted out the bill which became the Atomic Energy 
Act of 1946. The deliberations of the Special Committee were con- 
ducted in a tense atmosphere and no one who participated in them 
escaped the aftermath of recriminations when international con- 
ditions had deteriorated. Condon became a target for those who pro- 
posed legislation which would have placed atomic energy under 
military control. From this conflict arose the accusations directed 
against Condon by the House Committee on Un-American Activi- 
ties under the chairmanship of Congressman J. Parnell Thomas. 
Thomas charged that Condon was one of the "weakest links in our 
atomic security." This charge has since become a journalistic refrain, 
almost invariably repeated when Condon's name is mentioned in 
the newspapers, but no evidence has been adduced to support it, nor 
was Condon ever afforded an opportunity to refute the charge in pub- 
lic before the Committee, despite his many requests to be heard. 

In November 1945 he was appointed director of the National Bu- 
reau of Standards by President Truman, an appointment confirmed 
by the Senate without dissenting vote. He remained as director until 
October 1951, during which period the scientific strength and stature 



100 What Is Science? 

of this important government agency 'were greatly enhanced. Condon 
discharged his duties with admirable energy and imagination in the 
face of incessant attacks made upon him by members of Congress, 
political pundits and professional patriots. Fortunately he enjoyed the 
full confidence of the military departments and of the Atomic Energy 
Commission, the proof being the enormous increase in highly classi- 
fied research and development entrusted to the Bureau while he was 
director. This work included the development of new test equipment 
for measuring the properties of atomic bomb explosions, improve- 
ment of proximity fuses for use in the Korean war, establishment of a 
new laboratory in Corona, California, for Navy guided missiles and 
the setting up of two laboratories in Boulder, Colorado, one for re- 
search on thermonuclear weapons, the other for special studies of 
radio propagation effects vital to the planning and operation of the 
American radar defense network in northern Canada. 

In October 1951 Dr. Condon left the service of the government to 
become Director of Research and Development of Corning Glass 
Works. He held this position until his resignation in December 1954, 
when he returned to Berkeley, California to enter private practice as 
a consulting physicist and private research worker. Even during his 
private employment the attacks on him continued. In April 1952 his 
security clearance was suspended by Navy security officers. This cloud 
hung over him until April 1954, when a hearing of the entire Condon 
record was held in New York before the Eastern Industrial Person- 
nel Security Board, under procedures established by President 
Eisenhower. On July 12, 1954, the Board decreed that Dr. Con- 
don's clearance was "clearly consistent with the interests of national 
security." News of this verdict first became public on October 19; two 
days later the Secretary of the Navy ordered suspension of the clear- 
ance and "reconsideration" of the verdict by the Board. A Defense 
Department spokesman inadvertently admitted to the press that Con- 
don's clearance had been revoked because the newspapers had given 
it publicity. 

Condon was president of the American Physical Society in 1946 
and president of the largest American scientific body, the American 
Association for the Advancement of Science, in 1953. His election to 
the presidency of the AAAS was in part a tribute to Condon's scien- 



about Edward U. Condon 101 

tific stature, in part an affirmation by the entire scientific community 
of confidence in his integrity. 

I have gone out of my way to set before the reader a few of the 
main facts involved in Condons ordeal. I have done this for two rea- 
sons: first, because he has been my friend since we served together on 
the Senate Special Committee, he as scientific adviser and I as its 
counsel; second, because it is important to make known at every 
opportunity how well he has served the community and how well he 
has been repaid for his efforts. 



PHYSICS 

EDWARD U. CONDON 



In 1926, when the principles of quantum mechanics were being dis- 
covered, the great Gottingen mathematician, David Hilbert, re- 
marked that "physics is becoming too difficult for the physicists." The 
particular mathematical difficulties that prompted this witticism have 
been largely cleared up in the quarter century since then, but little 
progress has been made in interpreting the fundamental problems of 
atomic theory; meanwhile, experimentation has opened vast new areas 
of complexity. On balance, Hilbert's judgment is at least as true today 
as it was when he made it. 

If physics is too difficult for the physicists, the nonphysicist may 
wonder whether he should try at all to grasp its complexities and am- 
biguities. It is undeniably an effort, but probably one worth making, 
for the basic questions are important and the new experimental re- 
sults are often fascinating. And if the layman runs into serious per- 
plexities, he can be consoled with the thought that the points which 
baffle him are more than likely the ones for which the professionals 
have not found satisfactory answers. 

The subdivisions of science are somewhat arbitrary. Physics con- 
cerns itself with matter and energy in all their general manifesta- 
tions. It started to develop in a systematic way with the study, by 
Galileo, Kepler and Newton, of mechanical motions of large bodies. 
This was only about three centuries ago. Later it became interested 

102 



Physics iu*J 

in electric and magnetic forces and in the nature of light, including 
the invisible infrared and ultraviolet radiations and the more re- 
cently discovered X rays. It deals with heat and the thermal proper- 
ties of matter. Up to 1900, most of the study was carried on without 
regard to specific theories about the atomic constitution of matter. 
The work of our century has centered upon the development of a 
highly detailed and quantitative theory of atomic structure, the re- 
working of all of the older physics in terms of atomic concepts, and 
the exploration of new fields, particularly the phenomena of nuclear 
physics, under the guidance and stimulation of the fundamental 
theoretical ideas. 

Physics is closely linked with all other sciences. Astronomy in- 
terprets its results according to physical principles and so does geol- 
ogy. Chemistry makes increasing use of the results of modern physics. 
Whether or not life is ultimately explainable in terms of physical 
principles alone, living things are made of matter and the biologist 
must therefore take physical knowledge into account. 

Our era is witnessing an unprecedented activity in physics. The 
number of skilled investigators and the amount of elaborate and re- 
fined apparatus at their disposal is greater today than at any other 
time in the world's history. But despite the vast amount that has 
been learned there is no indication man is approaching the limits of 
physical knowledge. The possibilities for investigation are number- 
less and that is what makes the subject so thrilling to research physi- 
cists. 

The major discoveries made in the first half of the century suggest 
the present scope of this science: the quantum character of light 
energy (Max Planck and Einstein), the theory of relativity (Ein- 
stein), the nuclear structure of the atom (Lord Rutherford and Niels 
Bohr), interpretation of the light-emitting properties of atoms (Bohr), 
discovery of the wave and probability properties of matter (Prince 
Louis de Broglie, Erwin Schrodinger and Max Born), of heavy hy- 
drogen (Harold Urey), of the neutron (Sir James Chadwick) and 
of means of producing artificial transmutations of the elements (Sir 
John Cockroft and Ernest Walton, Fr&teric Curie-Joliot, Enrico 
Fermi and others). And the discovery of a whole family of new kinds 
of subatomic things which, unlike "normal" matter, can be created 



104 What Is Science? 

and destroyed (Carl Anderson, Hideki Yukawa, C. F. Powell and 
others). 

The purpose of this essay, then, is to try to take stock of the meth- 
ods and problems of modern physics. And it must emphasize at the 
start that, however abstract the ideas may seem, physics at all times 
endeavors to arrive at a set of principles and concepts which can be 
used in turn to describe the directly observable events of the material 
world. We are discussing things which can be made to happen, and 
which have been seen or otherwise observed to happen, by persons 
who have built and operated the necessary apparatus with the neces- 
sary skill. Since all observations of crucial importance have been re- 
peated and confirmed by different investigators, the possibility of the 
data being seriously in error because of subjective distortions is ex- 
tremely small. 

Physics is, however, much more than a description of apparatus 
how it was built and operated and of the raw data of observation 
thus obtained. The interpretive side of the science seeks to relate 
direct observations to a logical framework of concepts. This frame- 
work is periodically revised and extended to bring wider classes of 
data within its scope. Interpretation is important because it econo- 
mizes the mental effort needed to provide an accurate and embracing 
description of the facts, and because it suggests the making of obser- 
vations in areas never previously studied and devises "crucial" experi- 
ments that is, tests for the validity of alternative conceptual schemes 
which seem in advance to provide equally good explanations of what 
is known. In short, theories underly the program of experiments and 
experiments are used to judge the merit of theories. 

The physics of this century has set itself the task of interpreting 
all observed phenomena in terms of the behavior of atoms and 
molecules, and the electrical particles electrons, protons, etc. of 
which they are composed. It was characteristic of the older physics 
that not only were phenomena observed on a scale comparable to the 
size of our own bodies, but mostly they were discussed according to 
a conceptual scheme of very much the same scale. It is characteristic 
of the new physics that, while the observations must necessarily con- 
tinue to be made with apparatus big enough for our hands to manip- 
ulate and our eyes to see, the purpose of the experiments is to sup- 



Physics 105 

ply details about a conceptual scheme disposed on such a fine scale 
as to be incapable of direct visual observation. It is a scheme which 
can be pictured only in the mind's eye, using linear magnifications in 
thought which range from one hundred million to one on up to 
about one million million to one. 

The modern physicist and anyone who would understand what he 
is up to, must therefore learn to work in two worlds. One is a world of 
brass and glass and wax and mercury and coils and lenses and vacuum 
pumps above all a world of electronic amplifiers and photo-multi- 
plier tubes. The other is a world of visualization and creative imagi- 
nation, dealing with concepts and constructs appropriate to atomic 
dimensions (or, in cosmology, to a domain too vast to be encom- 
passed by direct human perception). In this second world the atomic 
nucleus is a little hard ball, about 10~ 12 cm in diameter; 1 it carries 
an electric charge and is made up of a number of smaller particles, 
some having electric charges (protons) and some without electric 
charge (neutrons). Negatively charged particles (electrons) revolve 
around their nuclei at distances ten thousand times greater (10~* 
cm) than the nuclear diameter. The detailed behavior of these elec- 
trons accounts for the chemical behavior of the atom, for its light 
and X-ray emitting and absorbing properties, for its magnetic prop- 
erties and many other distinguishing qualities. 

The first goal of the beginning student is to keep both these worlds 
in mind at once. He has to learn how the world of direct observation 
serves as the means of indirect observation and controls his pictures 
of the atomic world. This problem is particularly difficult for the 
general reader who merely wishes a reasonably accurate and honest 
guide to what physicists are thinking. Popular writers, who cannot be 
sure that their hold on the reader's attention is either firm or lasting, 
are tempted to offer merely a pictorial account of how things look 
in the world of nuclei, electrons and quantum jumps. They do not 
try to give the reader any idea of our methods of direct observation 
into the world of atomic dimensions. To cover this side as well 
would double the length of the story and require that the reader be 
introduced to some highly complicated apparatus. 

1 Throughout this essay negative exponents are used. Thus 10- 8 = 00.001; 10~ 7 = 
00.0000001: lO-i 2 = 00.000000000001. 



106 What Is Science? 

Physics, perhaps more than any other science, expresses its observa- 
tions in numerical terms. Measurements and techniques of measure- 
ment are never far behind the purely descriptive phase when any 
new branch of physics is opened up. A specialty within the science, 
mathematical physics, formulates the laws of physics mathematically 
and deduces from such general laws special consequences which 
can be put to the test of experiment. Mathematical analysis is one 
more stumbling block for the person who would achieve a general 
understanding of modern physics without going deeply into the sub- 
ject. Many of the concepts of physics are so closely bound up with 
the mathematical way of describing them that it is hard to give them 
any other kind of description. A good example is electron spin. In 
many respects an electron behaves like a top spinning on its axis, yet 
the exact spin behavior is very different from that of the tops chil- 
dren play with. 

The nineteenth-century physicist sought to interpret the forces 
acting between electric charges, and between magnets, by postulating 
a space-filling stuff, the ether, which was imponderable, since solid 
bodies could move through it freely, but which, nevertheless, could 
exert forces by the action of tensions along the lines of force and 
pressures at right angles thereto. 2 The model was like an elastic solid, 
the behavior of which had already been fully described by mathemat- 
ical physics, and the plan was to relate electromagnetic phenomena 
to the already understood behavior of elastic solids. 

At first this analogy was taken quite literally, but after a time 
physicists began to regard it more as a symbol than as a statement of 
fact. They came to see that the essential thing was the construction 
of a logical, self-consistent theory of the electromagnetic field, one 
whose predictions could be checked by detailed quantitative experi- 
ments. Such a theory might be aided in its initial stages by reference 

*The seventeenth-century physicist Christian Huygens, who developed the wave 
theory of light, was one of the first to postulate the existence of an all-pervasive 
ether, building on earlier ideas of Rene' Descartes and Robert Hooke. By the end 
of the nineteenth century all kinds of marvelous properties were attributed to it. 
This stuff, said Sir Oliver Lodge, can vibrate light, can be "sheared" into positive 
and negative electricity, forms the matter of the universe by arranging itself in 
whirls, and "transmits by continuity and not by impact every action and reaction 
of which matter is capable/' 



Physics 107 

to an elastic solid. But the fact that the two distinct sets of physical 
phenomena are governed by mathematical equations of nearly the 
same structure does not justify the conclusion that one of them is the 
ultimate reality in terms of which the other is to be explained. 

Thus, because electromagnetic forces are in many ways analogous 
to the forces transmitted by stressing special types of elastic solid, it 
does not follow that electromagnetic forces are "really" transmitted 
through the agency of such stresses in an all-pervading space-filling 
solid "ether." Once it is realized that the mental picture of a solid 
ether is scaffolding rather than the real edifice, a considerable change 
in outlook occurs. The constructor of theories is no longer bound by 
the details of the original model. He may depart from it and con- 
sider more general viewpoints. He is not merely free to do so, he must 
do so if he is to be productive. 

How then is the theorist to be limited and guided? May he just 
write down any kind of mathematical relation? No, for he must rec- 
ognize certain broad principles by which all physics is believed to be 
governed. 

For example, it is generally assumed that, given the same set of 
circumstances, physical phenomena will happen in the same way to- 
morrow as they happened today or yesterday. This means that 
mathematical statements about the laws of physics must not contain 
any reference to an absolute value of time, such as the total time 
elapsed since the creation or some other event of basic importance. 

Time itself cannot occur as a mathematical variable in the equa- 
tions, but only differences of time between events related to the 
phenomena under consideration. The basis for this conclusion is ex- 
perimental: phenomena do recur in the same way under similar cir- 
cumstances when the experiments are made on different dates on the 
calendar. 

A little reflection will show that the actual experimental basis for 
this conclusion is rather slim. Science is so new that most of the 
matters to which we would like to apply the principle have been 
under observation for less than a century. How then can we be sure 
that the laws derived from today's studies have been exactly the same 
at all times in the past, and will remain so in the indefinite future? 

Thus, we estimate the age of rocks by their helium content, sup- 



108 What Is Science? 

posing this to have accumulated from radioactive disintegrations 
which occurred over the past billion years at the same rate as today. 
We cannot prove that the rate has been steady, but, since we know 
of no reason to assume that it has changed or will change, it is a 
convenient working hypothesis to assume that it has not and will 
not. 

Similar remarks may be made about the necessity for stating the 
laws of physics without reference to the absolute position in space, 
or the orientation in space of the apparatus with which observations 
are made. These principles of the homogeneity and isotropy 3 of space 
further limit the kind of mathematical relations that can occur in 
quantitative descriptions of physical phenomena. They also have some 
limited, direct empirical validity. But mostly they are assumed to be 
true because no observations contradict them. 

The kind of thinking that gave conscious recognition to such prin- 
ciples was gradually gaining ground before 1905. In that year it re- 
ceived a great impetus from Einstein, who applied it boldly and 
radically to a new field in his first paper on what is now known as 
the theory of relativity. The laws of electromagnetic phenomena, as 
we have just noted, were formulated in terms of the model of an 
ether somewhat like an elastic solid filling all space. If such a solid 
had a real existence, then there would be meaning to the question 
of absolute rest or motion: a body would be said to be absolutely 
at rest if it were not moving with respect to the ether and its absolute 
motion would be the direction and speed of its motion relative to 
the ether. 

Lacking some such absolute standard, one may speak only of the 
relative motion of one body with respect to another, and the idea 
of absolute rest or motion is devoid of observational content. In the 
latter part of the nineteenth century, light was regarded as a wave 
motion propagated in the space-filling solid ether. It was natural on 
this view to suppose that the content of an optical phenomenon 
would depend on whether the light-source and the observer of the 
light were at rest with respect to the ether or moving through it. 

A most sensitive experiment designed to test this point is known 
A space is isotropic if it possesses the same properties in every direction. 



Physics 109 

as the Michelson-Morley experiment, 4 first carried out in 1883 and 
repeated many times thereafter. The apparatus used, an interfero- 
meter, is shown schematically in Figure 1. It is rigidly built of steel 
bars on a stone foundation, but it is floated in a large tank of mer- 
cury and can thus be turned easily without suffering distortions or 
vibration. On this floating platform is mounted a source of lights 
part of whose ray is made into a parallel beam by the lens D. The 
parellel beam strikes a thinly silvered mirror at A, and is there split 
into a reflected beam going to B and a transmitted beam going to C. 
At B and C these two partial beams are reflected back on them- 
selves by mirrors. They then return through A and are combined in a 
single beam which strikes the lens E which brings it to a focus 
for observation. One adjusts the apparatus so that B and C are at 
the same distance from the mirror A. Suppose now that the ap- 
paratus is oriented so that AC is parallel to the direction of motion 
of the earth through the ether; AB must then be perpendicular to that 
direction. 




Source 



V 
'V'Obswver 

Fig. ] Apparatus for the Michelson-Morley experiment 

4 Named after its designers, the famous American physicist Albert Abraham Michel* 
son (1852-1931) and the American chemist Edward Williams Morley (1838- 



110 What Is Science? 

Then according to the theory of wave propagation the travel-time 
of the beams over the two equal paths should be slightly different, 
just as if two swimmers were required to swim an equal distance in 
a swiftly flowing river, one across and back, the other, downstream 
and back. The cross-river swim would not take as long as the up 
and downstream journey (because what the swimmer gains in time 
going downstream is more than offset by what he loses coming 
back) and, similarly, it was supposed that the two beams of light, 
one traveling with the earth's motion through the ether, and the 
other at right angles to its motion relative to the earth, would not 
arrive at the same time at the end of their journey. Since it was not 
known which was the direction of the earth's motion through the 
ether, the observations in the actual experiment were made with the 
apparatus turned in various directions in the laboratory; besides, the 
laboratory itself was turning in space with the rotation and annual 
orbital motion of the earth. The expected effect would of course be 
small because the speed of the earth in its orbit is only one ten- 
thousandth of the velocity of light and the theory indicates differ- 
ences in the two speeds of propagation of the order of the square 
of this quantity or only one part in one hundred million. Neverthe- 
less the apparatus was built with such precision that an effect of 
even this small magnitude would be clearly observable. 5 

But the experiment, though many times repeated and many times 
checked, gives no indication of the earth's motion with respect ta 
the supposedly stationary ether. This result flatly contradicted the 
ideas of the period. But when the concept of absolute motion irn 
space can find no support in careful and repeated observations de^ 
signed to detect it, the concept not only becomes of doubtful value 
to physics, but may even be responsible for wrong conclusions and! 
the frustration of progress. 

Einstein was bold enough to recognize that all the contradictions 
Could be removed by postulating as a basic law of nature that the 
velocity of light must appear the same to all observers irrespective of 
the state of motion of one observer relative to another. This was 

* In the difference in position of the so-called interference fringes, alternate bright 
and dark bands, produced by the rejoining of light waves. 



Physics 111 

certainly a clear-cut statement of the experimental evidence. But it 
was a statement which defied the mathematics of electromagnetism 
as then developed and, certainly again, that mathematics had a good 
deal of truth in it, for it was being used successfully to design elec- 
trical equipment. 

Einstein showed that the difficulties were related to uncritical as- 
sumptions in the basic technique of space and time measurements. 
Length measurements in the simplest instance are made by laying a 
rigid measuring rod alongside the space interval to be measured. 
Time measurements are made by noting the readings of a clock at 
the beginning and end of the time interval in question. The crux of 
the problem revolves about the exact way in which two observers, 
A and B, who are in uniform relative motion with respect to each 
other, are to compare space and time measurements which they make 
of the same set of natural phenomena. In particular, they must have 
some way of comparing their clocks and their measuring rods. 

The most direct way of comparing the measuring rods would be 
for B to send his to A's laboratory and have it laid along A's measur- 
ing rod to see if the distance markings correspond. But after this 
process has been carried out, B's measuring rod has to be accelerated 
from its state of rest in A's laboratory in order to get it up to the 
right speed to return it to B's laboratory. We know that forces must 
be applied to the solid material to speed it up and we have no right 
to assume that these do not introduce a change in the length of the 
rod we have just checked. In fact, the Dublin physicist George Fran- 
cis Fitzgerald and the Dutch physicist H. A. Lorentz independently 
made the bold assumption that a moving rod contracts in length in 
the direction of its motion. Although this contraction could be in- 
ferred from Clerk Maxwell's theory of electromagnetism and the 
electrical structure of matter, the concept was regarded as no less 
fantastic than the Michelson-Morley result, and physicists were re- 
luctant to accept one bizarre notion as explanation of another. 

Similar critical remarks might be made about any procedure for 
comparing B's clock with A's clock, which involved delivering B's 
clock to A's laboratory in order to compare the rates at which they 
are running. When after being checked in A's laboratory B's clock 



112 What Is Science? 

is accelerated for the purpose of delivery to B, we have no right to 
assume that it continues to run at the same rate as it did when it was 
being checked. 

To avoid these critical difficulties, Einstein proposed a way whereby 
A and B could compare their clocks and measuring rods without 
actually bringing them together. 6 His method involves the sending of 
light signals back and forth between the laboratories of A and B 
while they are in relative motion. In this case the very process of 
comparing measurements reproduces the arrangements of the Michel- 
son-Morley light-transmission experiments. 

But the fact that Einstein's proposal afforded no escape from the 
dilemma we have been considering was in itself a discovery of the 
greatest importance. For it supported the conclusion which was one 
of Einstein's most striking insights that it is inherent in the nature 
of the measuring process that the phenomena of propagation of light 
appear the same to all observers no matter what their state of uni- 
form relative motion. In other words the Michelson-Morley result 
follows inevitably from the method of the experiment, and even the 
Lorentz-Fitzgerald concept turns out to be true though the con- 
traction has nothing to do with the ether. 

In terms of mathematical relations this can be summed up as fol- 
lows: A will have done basic experiments and will have deduced 
from them a set of rules for calculating electromagnetic and optical 
effects in terms of the space and time intervals which he measures 
in his laboratory with his equipment. Then B will do the same thing 
with regard to quantities measured by him in his laboratory and he 
will find that the mathematical laws describing his observations have 
the same form in terms of his observed space and time intervals as 
A found in terms of his. 

We describe this property by saying that the laws have an in- 
variance of form with regard to the space and time data of the 
two relatively moving observers. 

These ideas seemed radical and revolutionary at the time. They 
showed the physicists that they had been guilty of a superficiality in 

6 The reader will understand, of course, that we are discussing conceptual, not 
actual, experiments, and that Einstein's was a theoretical solution of a theoretical 
problem. 



Physics 113 

analyzing the process of comparing measurements in two different 
laboratories in uniform relative motion. This had hitherto been re- 
garded as a matter too obvious for careful procedure. 

There was another reason why these ideas were revolutionary. The 
laws of mechanics, formulated by Isaac Newton in 1660, were re- 
garded as one of the most firmly established parts of physics. The 
laws of electromagnetism were discovered some two centuries later. 
Naturally men did not feel as confident of their correctness as they 
did about Newton's teachings. But the new ideas of Einstein de- 
manded the change and modification, not only of the later laws, but 
also of Newton's hitherto unchallengeable writ. 

The necessary corrections were so small that under ordinary cir- 
cumstances they had no observable consequences. It was as if men, 
long believing that certain lines were absolutely straight, were told 
that they really contained a curvature too slight to be noticed. Still, 
it is understandable that the situation caused emotional disturbances 
among physicists; there is a tremendous gap between our ideal of the 
Perfect and of the Very Slightly Imperfect. 

The velocity of propagation of light signals which, according to 
the experimental evidence, is the same to all observers, is about 
186,000 miles a second. That is an extraordinarily great velocity com- 
pared with any of the speeds of normal experience, even of the 
motion of the earth and other planets in their orbits. It turns out 
that the changes in the old mechanical laws of Newton which were 
a consequence of Einstein's theory of relativity involved corrections 
of the order of (v/c) 2 where v is the speed of motion of the body 
being studied and c is the speed of light. For all ordinary experience 
the difference in the predictions of the two distinct theories was 
less than one part in a billion, a much smaller quantity than the 
accuracy or sensitivity with which even the most precise measure- 
ments of this kind can be actually carried out. Therefore the differ- 
ence was of no practical consequence in regular applied mechanics. 
But the revision of ideas involved was so basic that it became of the 
utmost importance to devise experiments in which the Newtonian 
and Einstcinian theories could be submitted to observational test. 
Because the differences become appreciable only when particles are 
moving with speeds comparable to that of light (even when a particle 



114 What Is Science? 

is going a tenth the speed of light the difference between the 
theories is only about one per cent) this required study of the be- 
havior of focused beams of electrons moving in a high-vacuum tube 
and deflected by electric and magnetic forces. Many such observa- 
tions supported the Einstein-modified equations of particle mechan- 
ics rather than the original laws stemming from Newton. 7 

One consequence of the Einstein equations of motion was the 
new principle that no body can move faster than the speed of light. 
The rate of increase of speed of a body when acted on by a con- 
stant force is the quotient of the force divided by the mass of the 
body, which is a measure of its inertia. On Newtonian views the mass 
is the same at all speeds. On the Einstein view the mass increases 
with the speed, with the result that the ability of a constant force 
to increase the speed becomes steadily weaker as the speed increases. 
At first this effect is very small, but it rapidly becomes a major 
factor as the particle's speed rises and it completely frustrates the 
accelerating force when the speed of light is finally attained. Einstein 
also observed that the increase in inertia of the body was exactly 
proportional to the increase in its energy of motion; he was thus led 
to the more general deduction that energy of all forms has inertia and 
that any system has more inertia when its energy content is in- 
creased. 

This result had hitherto escaped discovery because, for example, 
in the most energetic chemical reactions, the decrease in total mass 
or inertia due to the energy released amounts to only about a bil- 
lionth part of the whole. But many years later, with the advent of 
the study of nuclear transformations, the deduction was brilliantly 
confirmed; for in these drastic processes the energy changes are some 
million times greater per unit weight of reacting substance, and the 

T This discussion of Einstein's postulates differs somewhat from the usual popu- 
larizations. In more familiar terms and very briefly the two essential assumptions 
of his special theory are: (1) The velocity of light in a vacuum is constant and 
independent of the motion of the source, and therefore independent of relative 
velocity of source and observer; (2) If two systems are in uniform motion with 
respect to each other, then all phenomena in one system run their course with 
respect to the other system according to the same laws as with respect to the first; 
which is to say that all measurements within a system are unaffected by its (un- 
accelerated) motion, or to put it yet another way, that no measurements con- 
ducted entirely within a system will disclose whether or not it is moving. 



Physics 115 

accompanying changes in mass, of the order a few tenths per cent, 
are easily observed and of dominating importance to complete under- 
standing. 

The energy that is given to an electron in an X-ray tube operating 
at 500,000 volts is enough to double its inertia. Therefore X rays that 
are now in daily use in many hospitals are produced by electrons 
whose behavior is strongly affected by the consequences of the fa- 
mous E=mc 2 formula relating the energy, E, to its equivalent mass 
m, where c is the velocity of light. Even in the picture tubes of 
millions of home television receivers, the electrons have about five 
per cent extra mass due to the energy of motion with which they 
strike the fluorescent picture screen. 

Einstein's successful challenge of Newtonian physics is a sharp re- 
minder that we must keep clearly in mind the actual range of verifica- 
tion of our known physical laws and be prepared to modify our 
initial formulations when these are proved no longer adequate to 
describe a wider range of phenomena. 

Common sense is prepared for the idea of small and distinct 
particles moving in ways described by laws of motion such as New- 
ton's or perhaps even Einstein's modification of them. Moving balls, 
planets and missiles are familiar objects in daily life. Likewise com- 
mon sense will agree that effects may be propagated from one place 
to another by an oscillatory train of waves such as those which spread 
out on the surface of a still pond when a stone is dropped into it. 
Thus a physical effect may go from one place to another by the 
flight of a steady stream of projectiles, or it may travel from one 
place to another by the propagation of waves. 

Three centuries ago, when men speculated about the nature of 
the influence we call light, that which proceeds from a candle to the 
eye, some believed that the candle projects outward a stream of mi- 
nute corpuscles of light which fly through space and even through 
dense transparent materials such as glass. This is the corpuscular 
theory of light. 

Others thought that the influence called light was a wave motion. 
These waves were supposed to travel in a space-filling material called 
the luminiferous ether, which was later identified with the space- 



116 What Is Science? 

filling ether presumed to be the means of propagating electric and 
magnetic effects. This was the wave theory of light. 

Newton favored the corpuscular theory, and Christian Huygens, a 
great Dutch contemporary of his, favored the wave theory. 

The shadow of an object in light from a small source is quite 
sharp (Fig. 2). There is an abrupt break between the surround- 
ing brightness and the cast shadow. This is the pattern to be expected 
if light consists of a stream of particles moving out from the source 
in straight lines 1 . 



Source 




Bright 



Dark 

I Opaque object 

Fig. 2 Corpuscular view: Shadow cast on screen by opaque object has 
sharp edge if light source is small or very distant. 

How waves behave when they encounter an obstacle is familiar to 
us from observing the ripples on a pond. Water waves are not cut 
sharply by an obstacle; instead, they bend partially around it and 
then continue, so that the wave motion can be seen on the side of 
the obstacle away from the wave source. Thus if light were propa- 
gated by wave motion, we should expect the shadows cast by objects 
to have soft, diffused edges. The observed sharpness of shadow edges 
seems, therefore, to support the theory that light consists of a stream 
of particles. This course of reasoning was decisive in leading Newton 
to reject the wave theory (Fig. 3). 

But the problem is not so simple. Experiments performed many 
years after Newton revealed that the bending of waves into the re- 
gion behind an obstacle is only noticeable when the obstacle is small 
compared with the length (distance from crest to crest measured in 
the direction of travel) of the waves; in the opposite case, where 
the wave length is small compared to the obstacle, the wave motion 
is inappreciable and apt to escape detection. In other words if the 



Source 



Physics 117 
Bright 



J..IU1 

I Shadow 

| Opaque object aril 



Transition 
region 



Fig. 3 Wdve view: The shadow does not have a sharp edge, but some 
light penetrates into the transition region. 

wave length is small compared to the object casting the shadow 
the most common occurrence only the most delicate tests will help 
clarify the issue between the corpuscular and the wave theory of 
light. 

When experimental techniques and instruments had been suffi- 
ciently refined, a higher level of understanding was attained. Phys- 
icists were able to show that light really does bend somewhat into 
the shadowed region. The phenomenon is called diffraction. To be 
sure, a person who was determined to hold on to his belief in the 
corpuscular theory might start speculating that the material of the 
opaque screen exerts attractive forces on the light corpuscles that fly 
past near the edge of the screen and bends their trajectories into 
the region that otherwise would be the dark shadow. But exact and 
detailed studies of how much the light is bent into the shadow when 
passing objects of various shapes and sizes gave results that could not 
be accounted for in this way. On the other hand, they could be 
beautifully described according to the theory of wave propagation on 
the supposition that light of a particular color consists of waves of a 
particular wave length. Blue light on this view has a wave length 
of close to 4 X 10~ 5 cm; red light, at the other end of the visible 
spectrum, moves in waves about twice as long. The invisible ultra- 
violet radiations have a wave length shorter than the violet and 
the invisible infrared radiations have wave lengths longer than the 
red. 

It is the smallness of these wave lengths compared with the million 



118 



What Is Science? 



times greater wave lengths for the ripples on a pond that made the 
diffraction effects more difficult to observe and resulted in their being 
hidden from the eyes of man so long. Nevertheless, now that these 
matters are more thoroughly understood, optical effects which di- 
rectly exhibit the wave nature of light may be easily observed. 





Indicating the evenly spaced threads Showing the pattern of light of a 
of the weave of silk cloth. distant small source, like a street- 

light, observed through such a 
closely woven cloth. The central 
image is round and white. The 
others are elongated and show rain- 
bow colors with the red end away 
from the central image. 

Look at a distant street light through a silk umbrella or a tightly 
stretched silk handkerchief held several feet in front of the eyes. 
Instead of seeing only the ordinary direct image of the street light, 
perhaps a little blurred by scattering in the fabric, you will see two 
additional series of images extending away from the central direct 
image in two perpendicular directions. The directions in which these 
images extend will be easily found to be along the directions of the 
threads of the fabric. 

These additional images are quantitatively explainable on the wave 
theory of light. The essential thing here is that a wave motion 
spreads out from the distant street light and impinges on different 
parts of the fabric so that parts of the wave motion get through to 
the other side by going through the different regularly spaced open- 
ings on the fabric. The ideas involved may be more simply considered 
if we suppose that the light from the distant source goes through a 
screen having two very narrow and closely spaced slitlike openings 



Physics 1 1 9 

in it as indicated in Figure 4. If one wants to go to the trouble he 
can make such an opaque screen from a densely-exposed photo- 
graphic plate, using a razor blade to rule two very narrow slits on it 
quite close together. The razor blade cuts away a narrow strip of the 



Slit 





siit 



Fig. 4 Passage of light through a screen having two slit-shaped openings. 

darkened film and allows the light to get through. When such a plate 
is used to view a distant light source it will be found that the direct 
image is also accompanied on each side by several weaker side images 
in directions at right angles to the direction of the rulings on the 
plate. Careful observation of the side images either as seen through 
the silk umbrella or as seen through the two-slit plate will show that 
the central image is white, but that the side images are colored like the 
rainbow, with the red end of the spectrum at the end farthest away 
from the central image. 

Now we can return to the consideration of Figure 4. Suppose the 
screen is set up in such a way that slit A and slit B are at the same 
distance from source S. This is not essential but simplifies the dis- 
cussion. Then the crests of waves from S will reach A and B at the 
same time. On the other side of the screen two new sets of waves 
will spread out from A and B as new centers and these will be 
synchronized because they are the result of feeding the new sources 
A and B with light coming from the source S. Next we have to 
recognize that what affects any light-detecting device such as the 



120 What Is Science? 




The central part of the picture shows how a very distant and small source 
of light appears when viewed through a small rectangular opening held 
at arm's length from the eyes, the rectangular opening being the shape 
shown in the lower right-hand corner. Note that there are a whole series 
of images extending in each direction, and that they are more closely 
spaced in the direction corresponding to the long dimension of the rec- 
tangle. If the picture were reproduced in color it would be seen that the 
more or less overlapping images of the separate blobs of light away from 
the central image are colored with the rainbow colors, the red end being 
farthest away from the central image. Such extra images and dozens of 
other similar experiments with light going through openings of other 
shapes are interpreted as indicating that light is propagated as a wave 

motion. 

eye is the resultant amplitude of all the different waves which reach 
it. Suppose C is a point equidistant from A and B. Then crests of 
waves from A will arrive at C at the same time as crests from B 
and will reinforce each other to make bigger waves. Thus we may 
expect the brightest illumination at C even though it lies within the 
shadow of the screen between A and B and therefore on the corpus- 
cular view should be dark. Consider now what will be observed at a 
point C', a little above or below C. In moving from C to C' the 
distance from B is increased and the distance from A decreased. 
Suppose, in particular, that C' is so located that the difference be- 
tween AC and BC' is exactly half a wave length. Then at C' the 
crests of waves from A will fall on troughs of waves from B, and 
the waves will just cancel each other; in other words, assuming light 
is a wave motion, C' will be dark. Now move C 7 further up so that 
the difference between the distances from A and from B is equal 



Physics 121 

to a whole wave length. In this case, again, the crest of each wave 
from A falls on the crest from B, intensifying the light. As we con- 
tinue moving up C', it will alternately be light and dark as the 
differences between the paths is an integral multiple and an in- 
tegral-and-a-half multiple of a wave length. This special property of 
waves of reinforcing each other or destroying each other according as 
crest falls on crest or crest on trough is called interference. It ac- 
counts quantitatively for the light images seen through the silk um- 
brella. For example the reason the red end of the spectrum is farther 
out than the blue is because the red wave length is greater than 
the blue; so it is necessary to go farther out to get a half wave 
length path difference with red light than it is with blue light. 

During the nineteenth century a great many special cases of the 
behavior of light in going through obstacles having one or several 
holes of different shapes were analyzed carefully both theoretically 
and experimentally. The results were found to be quantitatively de- 
scribable in terms of the mathematical theory of wave propagation. 
Thus the wave theory of light became firmly established: students 
were taught that light is a wave motion and received good marks 
on examination papers for repeating this back to their professors. 

However, new phenomena began to be studied which pointed once 
more toward the corpuscular theory. Effects which I shall describe 
pointed strongly to the conclusion that a beam of light consists of a 
stream of particles of definite size, possessing energy and momentum 
content. Physicists were thus confronted with two independent sets 
of evidence. One set gave convincing "proof that light is a wave 
motion and the other gave equally convincing "proof 7 that a beam 
of light is a stream of corpuscles. Light is emitted and absorbed as if 
it were a stream of particles but it moves from place to place past 
obstacles as if it were a wave motion. Clearly there is truth in both 
models, and a synthesis of the two views into a unified picture is 
urgently needed. This wave-particle duality is an unsolved dilemma 
of modern physics. 

Before considering detailed effects, let it be observed that on the 
wave view the intensity of light is connected with the amplitude of 
swing of the waves; to be specific, it is proportional to the square 



122 What Is Science? 

of the wave amplitude. As a wave spreads out this becomes con- 
tinuously smaller with consequent reduction in the intensity of the 
light. On the corpuscular view the energy in the light beam is the 
total energy of a large number of independently moving corpuscles, 
called light quanta in modern terminology. The energy carried 




Fig. 5 The amplitude of a wave dies off inversely to the distance from 
the source as the wave spreads out in all directions. The intensity or bright- 
ness of the light is proportional to the square of the amplitude and so falls 
off with the inverse square of the distance from the source. 

by each quantum is always the same the decrease in intensity of 
the beam is a consequence only of the decrease in the number of 
particles crossing unit area in unit time. On one view the energy is 
continuously spread out over all the space occupied by the light 
beam; on the other it is localized in small bundles occupying a part 
of the total space, just as the molecules of a gas at ordinary pressure 
occupy only about one billionth of the total space which is filled by 
the gas. 

The photoelectric effect gave the first clue to the corpuscular na- 
ture of light emission and absorption. If a piece of metal, insulated 
from the ground, is charged with negative electricity, the charge will 
leak off through the air when light, especially violet and ultraviolet 
light, shines on it. In this simple version of the experiment the 



Physics 123 

effects are complicated by the action of the air layers which are 
absorbed on the metal. 8 Consequently, physicists who wish to study 
the photoelectric effect enclose the metal in a high-vacuum tube 
from which the gas can be removed to an extremely low pressure. 

The amount of charge which is set free from a metal surface is 
proportional to the intensity of the light falling on it. This fact is 
explainable either on wave or corpuscular views. But it is found that 
the leakage of negative charge from the metal comes about through 
the ejection by the light of negatively charged electrons. Measure- 
ments of the speed of ejection of these electrons show that the 
energy with which they are ejected is approximately inversely propor- 
tional to the wave length of the light used. Actually the energy of 
motion of the liberated electrons is a little less than such a rule 
would imply. Einstein in 1905 pointed out that this experimental 
result could be most simply understood if one supposed that the 
light energy was absorbed in definite quanta of energy, the energy 
of one quantum going to the individual act of liberating one elec- 
tron. The energy of one quantum was taken to be he/A, where h 
is a coefficient known as Planck's constant, c is the velocity of light 
and A is the wave length of the light. The observed energy of 
motion of the freed electron is less than this by an approximately 
constant amount because a part of the energy supplied by the light 
quantum is used up in releasing the electron from the attractive 
forces which normally bind it within the metal. 

Similar effects are observed when X rays are used instead of light 
to cause the ejection of electrons. The quantum effects are even 
more pronounced because the X-ray wave lengths are approximately 
ten thousand times smaller than those of visible light and therefore 
the energy in an X-ray quantum is some ten thousand times greater 
than in a visible light quantum. But because the wave lengths are so 

8 Although qualitative effects are easily demonstrated with the experiment done in 
air, exact measurements of the motion of the electrons ejected by the light re- 
quire that the metal be enclosed in a vacuum tube, both because of chemical 
actions of the gas of the air, especially moisture, on the metal which strongly 
change its ability to emit electrons, and also because if gas is present the electrons 
very quickly become scattered and attached to gas molecules, making it difficult 
to observe the speed with which they are thrown out. 



124 What Is Science? 

much smaller, it was for a long time impossible to observe, in the 
case of X rays, the diffraction and interference effects which give us 
our most decisive criterion for the wave nature of visible light. 

It happens, however, that the wave length of X rays is just about 
the same as the distance between the layers of atoms in layers in the 
regular arrangements that occur in crystals such as those of quartz 
or rocksalt. This means that interference effects such as those de- 
scribed for light going through the silk umbrella are observed when a 
beam of X rays is scattered by falling on a crystal. Instead of the 
scattered radiations going out from the crystal more or less equally in 
all directions, they are scattered only in certain specific directions. 
These directions are determined by relations between the X-ray 
wave length and the spacing of atoms in the crystal. Thus the effect 
can be used with a known crystal to determine the wave length of 
X rays from a variety of sources. Or it can be used the other way 
round to discover with X rays of known wave lengths exact in- 
formation about the arrangement of atoms in crystals whose geom- 
etry is not known. This diffraction of X rays by the orderly arrange- 
ment of atoms in crystals was discovered in 1912 by Max Von Laue. 
In such work the scattering is effected by electrons that are re- 
latively securely bound to the atoms of which the crystal is made. 

In 1922 Arthur H. Compton discovered another characteristic 
of the scattering of X rays by matter. He noticed, particularly when 
high energy X rays are scattered by lighter elements such as carbon, 
that the wave length of the deflected X ray is somewhat longer than 
that of the X ray before deflection, and that the amount of this 
Compton-shift toward longer wave length increases steadily from 
zero as the angle of deflection increases. Compton showed that this 
behavior was exactly what is to be expected from the quantum or 
corpuscular theory. If the X rays are tied up in quanta of energy, it 
is natural to suppose that these quanta also carry definite amounts 
of momentum. When they strike an almost free or loosely bound 
electron and are scattered, they rebound from it, Compton supposed, 
according to the same mechanical laws as those governing the col- 
lisions of billiard balls. At a very glancing blow the X ray is only 
slightly deflected in direction and gives up very little energy to the 
electron with which it collided. When the blow is more central it is 



Physics 1 25 

deflected through a wider angle and gives up more energy to the 
struck electron, losing thereby more of its own energy and thus hav- 
ing its wave length increased. 

This completed the duality. X rays which in respect of their being 
scattered by the tightly bound electrons in the regularly spaced atoms 
of a crystal behave like a train of waves of a definite wave length, 
also behave in respect of their scattering by loosely bound electrons 
as if they were little bundles of energy and momentum rather 
than continuously spread out waves, these little bundles or quanta 
obeying the ordinary laws of collision mechanics when they collide 
with an electron. In order to describe all of the phenomena it is 
necessary to talk some of the time as if the X rays are a wave 
motion and some of the time as if they are a stream of particles. 

There used to be a joke current among physicists that X rays 
were to be regarded as waves on Mondays, Wednesdays and Fridays 
and as quanta on the other days. In point of fact, however, the two 
aspects are so closely intertwined that no such neat separation of 
viewpoints can be effected; in Compton's experiments, for example, 
the scattering in carbon which is described by quantum or corpus- 
cular language is followed by another scattering of the same X rays 
by a crystal for the purpose of demonstrating that their wave length 
was altered in the first scattering. 

In the first decade of this century it had become clear that the 
atoms of matter contained small negatively charged particles called 
electrons. A great deal of attention was being given to the study of 
the naturally occurring radioactive elements, of which radium is the 
best known. Radium gives off spontaneously three kinds of radia- 
tions: gamma rays, which are a kind of high energy X rays of ex- 
tremely short wave length; beta rays, which are high speed electrons, 
and alpha particles, which are now known to be charged particles 
about 8000 times as massive as the electron. 

In 1912 Ernest Rutherford in England performed experiments in 
which he allowed a beam of alpha particles from radium to fall on a 
thin gold foil. He wanted to learn something of the forces by which 
gold atoms deflect the high-energy alpha particles from straight mo- 
tion through the foil. He found that the alpha particles were some- 



126 What Is Science? 

times scattered through more than a right angle, occasionally re- 
bounding almost straight back on striking the gold foil. From this he 
was able to calculate the amount of the force exerted by a gold atom 
on an alpha particle. The most natural thing was to assume that the 
force was electrostatic since the ordinary effects of collision could not 
account for the phenomenon. The gold atom, being neutral, must 
contain positive electricity as well as the negative electrons which 
other evidence had shown it to contain; the positive electricity would 
repel the positively charged particles. Before these experiments were 
performed there had been a tendency to suppose that the positive 
electricity was distributed uniformly over a sphere of about the same 
size as the whole atom. Rutherford's work proved that this was im- 
possible, for if the positive charge were thus spread out it could not 
exert a strong enough force on the alpha particle to reverse its direc- 
tion of motion. In brief, the experiments taught that the positive 
charge must be confined in a tiny particle, about one ten-thousandth 
the radius of the atom, which Rutherford called the nucleus of the 
atom. 

Thus originated the nuclear atom model which is the basis of all 
subsequent work in physics. Each atom consists of a central nucleus 
about 10~ 12 cm in diameter and carrying a positive electric charge, 
surrounded by enough electrons occupying a sphere roughly 10~ 8 cm 
in diameter to make the whole entity electrically neutral. The charge 
of the electron is accepted as 4.80 X 10~ 10 absolute electrostatic unit; 
the proton, the charged particle of the nucleus, has a positive charge 
equivalent to the negative charge of the electron but possesses a 
mass approximately 1,845 times as great. Different kinds of atoms are 
characterized by the magnitude of the electric charge on the central 
nucleus and, correspondingly, by the number of electrons surround- 
ing the nucleus. This is called the atomic number, Z, and ranges 
from one, for hydrogen, the simplest atom, up to 92 for uranium, 
and even higher for some of the atoms resulting from artificial trans- 
mutations. 

Niels Bohr of Copenhagen, then a young research student working 
with Rutherford, took up the idea of the nuclear atom. He combined 
it with the idea of emission and absorption of light in quanta, which 
had come out of photoelectric effect studies, and showed how the 



Physics 127 

characteristic spectrum of colors of light emitted by atoms in electric 
arcs and sparks could be given detailed and exact interpretation. 

To do this he had to make some radical assumptions about the 
motion of electrons in atoms. These constituted a much more severe 
break with Newtonian mechanics than the small corrections implied 
in Einstein's relativity theory of 1905. He assumed that mechanical 
systems could exist only in certain states of discrete energy values. 
That is, the atom could have certain "allowed" values of its total en- 
ergy: contrary to classical mechanics, it was supposed incapable of 
having a stable existence at other values of the total energy. He sup- 
posed that light emission occurred by the giving off of one light 
quantum when the atom passed in a transition from one stable en- 
ergy state to another one of lower energy. Thus the wave lengths of 
the characteristic light, as observed in a spectroscope, were a direct 
indication of the intervals between the allowed levels. 

These ideas were enormously fruitful in interpreting the spectrum 
of light emitted by atoms. It was soon found that they could be ex- 
tended to the analysis of X-ray spectra and also to the much more 
complicated spectra emitted by molecules. From 1912 to 1924 phys- 
icists were mainly occupied with working out the implications of 
Bohr's model. In the course of doing so, they added many exciting 
new details to the rapidly developing theory. In particular, they dis- 
covered electron spin that electrons behave like little magnets and 
spinning tops in addition to exerting force by virtue of their negative 
electric charge. 

Nevertheless, as Bohr repeatedly emphasized, the foundations of 
the development were far from definite, because he had not been 
able to give rules general enough to determine the allowed energy 
levels in all cases. Even the calculations on the next simplest atom 
after hydrogen, that of helium, having two electrons, went wrong. 

In 1924, Louis de Broglie made a suggestion in his doctor's thesis 
in Paris that opened the way for the next great advance. He asked 
whether the wave-particle duality of light might extend also to the 
fundamental particles of matter, whether there might be a wave as- 
pect to the energy of electrons, just as there was a by then well' 
recognized quantum aspect to the wave motion of light. He was not 
explicit about how an electron is accompanied by or associated with 



128 What Is Science? 

a wave motion. But he did suggest as a tentative hypothesis that the 
relation between the wave length of these waves and the momentum 
of the electron was the same as had been established for light and 
X rays. 

The way such a wave motion would limit the atom to particular 
energies was then to be regarded as similar to the way a violin string 
of definite length and tension can vibrate only in the particular fre- 
quencies known as its fundamental and overtones. The vibrations of 
the string must be such that an integral number of half wave lengths 
must be contained in the length of the string. Two years later Erwin 




Fig. 6 Forms assumed by a vibrating string vibrating at its fundamental 
frequency (a) and its first two overtones (b) and (c). In (a) the fre- 
quency is such that the string's length equals exactly one half wave length; 
in (b) and (c) the length is equal to two and three half wave lengths 
respectively. For a uniform string the frequency of (b) is exactly twice 
that of (a), so musically it is one octave higher. Other relations hold if 
the string is nonuniform. 

Schrodinger, then of Zurich and now of Dublin, gave a more specific 
and precise mathematical formulation of De Broglie's wave ideas. 
This summary went beyond Bohr's original formulation and was 
quickly found to accord with experiments in situations where Bohr's 
earlier formulations had gone astray. 

Soon thereafter C. J. Davisson and L. H. Germer in New York 
and G. P. Thomson in England independently performed crucial ex- 
periments on the scattering of high-energy beams of electrons by 
crystals which directly confirmed the wave nature of the electron by 
showing that the electrons are scattered in only certain definite direc- 
tions and that these are the ones to be expected from the scattering 



Physics 1 29 

of the De Broglie waves from a crystal. And again a short time later, 
experiments performed by Otto Stern in Hamburg proved that pro- 
tons, the positive nucleus of the hydrogen atom, were also scattered 
like waves from crystals. Thus the wave character of atomic particle 
behavior was firmly established. 

Another mathematical consequence of the difference between the 
behavior of particles and waves proved to be the key to under- 
standing the radioactive disintegration of natural radioactive materials 
such as radium, uranium and thorium. In classical particle mechanics 
the actions of forces on the particle may be described by giving its 
potential energy at each position in space. To this must be added 
the particle's kinetic energy to find its total energy, which remains 
constant throughout the motion of the particle. The kinetic energy 
is proportional to the square of the particle's velocity and is therefore 
essentially positive. It follows classically that a particle cannot move 
to a place where its potential energy is greater than its total energy, 
for this would require the kinetic energy to be negative. However the 
mathematics of wave propagation introduces departures from this 
rule. The rule is still approximately true in that the wave does not 
get very far into the classically forbidden region, the potential barrier,, 
but the essential point is that it can do so. 

This gives rise to a characteristic feature of atomic or quantum 
mechanics which was applied in 1928 independently by E. U. Con- 
don and R. W. Gurney in Princeton and George Gamow in Got- 
tingen to a quantitative interpretation of the way in which alpha 
particles are ejected from the nuclei of radioactive materials such as 
radium. This interpretation clinched the wave theory for nuclear par- 
ticles and provided the first detailed theoretical interpretation of any 
dynamic feature of the behavior of atomic nuclei. 

Figure 7 is a graph relating the energy of interaction of an alpha 
particle with the rest of the nucleus to the particle's distance from 
the rest of the nucleus. The scale of ordinates (vertical scale) is in 
MEV units, that is, million electron volts, where one million electron 
volts is the energy acquired by an electron in falling freely through a 
potential drop of one million volts; the scale of distance, on the ab- 
scissas (horizontal scale), is in units of 10~ 12 cm. 

At distances greater than about one of these units the entire en- 



130 What Is Science? 




12345 678 

Distance of a particle from rest of nucleus (Unit = 10'" cm) 

Fig. 7 Showing the Coulomb barrier around nucleus through which 
a-particle leaks in natural radioactive disintegration. (The shading, /////, 
indicates the barrier which, on the average, delays by a billion years the 
leakage of an a particle from the uranium nucleus, and the shading, 
\\\\\, indicates the much leakier barrier that permits the analogous spon- 
taneous disintegration of polonium to occur in about one millionth of a 

second. ) 

ergy of interaction consists of the electrostatic repulsion between the 
alpha particle and the rest of the nucleus, both of which are posi- 
tively charged. Curve (a) portrays the interaction with uranium, 
curve (b) with polonium; the latter curve is lower because the rest 
of the nucleus of polonium has 82 charge units after emitting n 
alpha particle, against 90 in the case of uranium. 

At distances less than one unit, strongly attractive forces come into 
play. These counteract the electric repulsion and cause a sharp dim- 
inution in the energy of interaction as shown by the almost vertical 
descent of the two curves. The over-all energy barrier is sometimes 
called the Coulomb barrier because it is mainly the result of elec- 
trostatic repulsions of the kind first quantitatively studied by the 
French physicist Charles A. Coulomb late in the eighteenth century. 



Physics 131 

The energy of emission of an alpha particle from uranium 238 is 
known to be 4.25 MEV, indicated in the figure by a straight line at 
this level. According to classical mechanics a particle possessing this 
energy could either exist inside the nucleus, or outside at distances 
greater than 6.2 units, where the total energy exceeds the barrier 
height, but could not exist in the region between (where the line is 
dashed), where the total energy is less than the barrier height. Classi- 
cally a particle situated inside would simply oscillate back and forth 
making about 10 21 collisions a second with the inside surface of the 
nucleus. 

But according to wave mechanics, such a particle has an extremely 
small, but nevertheless quantitatively calculable probability of escap- 
ing about one chance out of 10 36 at each collision with the wall. An- 
other way of saying this is that the particle will have to make 10 36 
tries to have a probable single success of slipping through; and since 
there are 10 21 collisions per second, it will take 10 36 ~ 21 or 10 15 seconds 
of oscillations, on the average, for the liberating event to happen.* 

It is as if the alpha particles were patrons of a gambling house in 
Las Vegas, each playing the slot machine 10 21 times a second. Im- 
agine the machines, which are aptly dubbed one-armed bandits, so 
rigged that the jackpot comes up on the average only once in 10 36 
times of play. Then any one player can look forward to pulling the 
handle 10 15 seconds (on the average) about a billion years before 
hitting the jackpot. Of course the jackpot pay-off for an alpha particle 
patron is to be thrown out of the gambling house at a terrific speed. 

In the case of polonium 208, the energy of the alpha particle is 
more than twice as great (8.95 MEV) and the barrier is lower, so the 
chance of penetration is about 10 23 times larger. In consequence at- 
oms of this kind have an average life before disintegrating of only 
one ten-millionth of a second instead of the billion years of geologic 
time represented in the average life of an atom of uranium 238. 

These researches were the basis of a new system of mathematical 
principles. It was called wave mechanics by some and quantum me- 
chanics by others, the latter term being more commonly used now- 

Here the argument rests on very roughly stated numbers, but actually it can be 
carried out to give quite accurate agreement with experiment. 



132 What Is Science? 

adays. Either term refers to the mathematical apparatus that describes 
the structure and behavior of atoms, molecules and nuclei, and which 
has arisen from the strange combination of wave and particle ideas 
whose development has just been sketched in outline. Many persons 
contributed to the full mathematical development, most prominent 
among them, perhaps, being P. A. M. Dirac of Cambridge, England 
and John Von Neumann of Princeton. 

Physicists now had a set of rules by which they could compute 
marvelously correct answers to definite questions, yet none of them 
felt very comfortable about the real meaning and significance of the 
rules he was using. I remember one day in 1928 when Professor 
Bergen Davis of Columbia said to me, "I don't think you young 
fellows understand it any better than I do. You just all stick together 
and say the same thing!" 

The deeper meaning of the wave-particle duality remained as much 
a puzzle as ever. In 1927 Max Born, then of Gottingen, supplied 
the interpretation which has been in use ever since although some 
physicists believe that it is no more than a makeshift which must 
eventually be supplanted by a more basic truth. This was Einstein's 
position. 

On Born's view, we may picture light and electrons and other such 
entities as "really" particles, but particles whose behavior is entirely 
different from those considered in classical mechanics such as tennis 
balls or the moon. Born sees the behavior of a particular particle as 
indeterminate. We are unable to follow its motion in detail. The 
most we can do is to calculate the numerical values of certain relative 
probabilities. These probabilities are to prefigure the possible ways 
of behavior, under observation, of a large number of particles; in 
other words the arithmetic is to tell us what we can expect to see. 
Thus, the wave motion aspect of the theory is interpreted as a device 
for predicting the relative likelihood of different things happening: 
where the wave motion is intense, the particles are more likely to be 
found. 10 

10 In atomic experiments the observations are always made on the behavior of large 
groups of particles. The results are therefore statistical, which is to say large num- 
bers of the more probable events are seen, fewer of the less probable. The pattern 
resembles that of observations of a human population; for example, if there is a 
greater probability of death from heart disease than tuberculosis, the annual sta- 



Physics 133 

This interpretation joins on smoothly with classical mechanics in 
the following way. When wave or quantum mechanics is applied to 
large particles the characteristic diffraction and potential barrier pen- 
etration effects of quantum mechanics become negligibly small and 
the probability rules predict that the particles will almost certainly 
behave as they do in classical mechanics. 

Soon after Born put forward the probability interpretation, Niels 
Bohr and Werner Heisenberg provided an analysis of how one might 
attempt the study of an atomic particle's motion with the same thor- 
oughness as can be applied to the observations of the moon. The 
analysis led to a startling conclusion. Classical mechanics requires 
that we know at the outset the initial position and velocity of each 
particle present, if we are to calculate the subsequent motion of each 
of them. Now to find the position of an electron one must shine light 
on it and try to see where it is by observing where the light is scat- 
tered. Owing to the wave nature of the light this procedure is capa- 
ble of localizing the electron only to a degree determined by the 
wave length of the light used. To get greater accuracy one would 
then tend to use light of shorter wave length. But when short wave 
lengths are scattered by an electron they cause it to recoil irregularly, 
as we noted in connection with the Compton effect. This recoil in- 
troduces an uncontrollable inaccuracy in our measurement of the 
electron's initial velocity. In other words, the very act of observation 
of the electron's position destroys in some degree the accuracy of our 
knowledge of its velocity. 

This analysis explains why a statistical interpretation, characterized 
by uncertainty, is forced upon us; it is an inescapable consequence 
of the fact that the thing observed reacts to the means we use to 
observe it. To avoid the reaction one must refrain from observation; 
then one remains ignorant of what happened. Statistical uncertainty 

tistics of cause of death will show that more persons have in fact succumbed to 
heart disease than tuberculosis. But an important distinction must be noted be- 
tween the statistics of human and particle populations. In mortality tables, the 
probabilities of death from various causes are in the first instance based upon 
observed frequencies; but in the probability estimates of quantum mechanics, 
the probabilities are initially inferred from fundamental theory, and later inter- 
preted (and confirmed) as relative frequencies of occurrence in a large ensemble 
of observations. 



134 What Is Science? 

seems to be the price that must be paid for gaining any knowledge 
at all. 

For a quarter century physicists have been warding off this conclu- 
sion; it is both so important and so unsatisfying that they are reluc- 
tant to accept it until every possible alternative has been refuted. No 
way out has yet been found. As of today we simply do not know 
whether the statistical interpretation of the wave-particle duality is 
inescapable because basic, or whether it will be discarded in some fu- 
ture theory which is fully deterministic. 

Many physicists in the past quarter century have been busy work- 
ing out the consequences of the ideas we have been discussing. 

First, the detailed analysis of visible and X-ray light-emitting prop- 
erties of atoms was almost completed. Immense amounts of precise 
experimental data have been closely correlated with exact theoretical 
predictions. 

Second, the same ideas were applied to the more complex task of 
interpreting light-emitting properties of molecules. This too is in sat- 
isfactory shape and continues to be studied in detail because it yields 
precise information applicable to chemistry. 

Third, the ways in which atoms are bound together to form solids 
came to be better understood. This is particularly true of the elec- 
trical properties of solids, of why metals conduct electricity easily and 
why materials like paraffin and quartz do not, and why some metals, 
notably iron, are easily magnetized. Physics has discovered and coped 
with the properties of solids called semi-conductors (silicon and ger- 
manium are good examples) which on contact with metals pass elec- 
tricity easily in one direction but not in the other. 

The barrier leakage interpretation of natural radioactivity has 
proved an important innovation. It pointed the way to obtaining ar- 
tificial nuclear transmutations with electrical machines limited to sev- 
eral hundred thousand volts, whereas earlier it was thought that ma- 
chines of a capacity of several million volts would be required. The 
experiment was tried in 1932 by Cockroft and Walton in Cam- 
bridge, England. When they directed a beam of protons which had 
been accelerated with a voltage of 500,000 volts against a target of 



Physics 135 

metallic lithium, they detected what seemed to be high-energy alpha 
particles like those from radium coming out of the target. Alpha par- 
ticles were known to be the high-speed nuclei of helium atoms, and 
the simplest explanation of the observation was that a hydrogen 
atom had reacted with a lithium atom to produce two helium atoms: 
in other words, a real transmutation of the elements such as had 
been for centuries the goal of medieval alchemists. 

Nuclear physics received two other great boosts that year. One was 
the discovery of the neutron by James Chadwick in England. The 
other was the discovery of the heavy isotopic form of hydrogen, now 
called deuterium, by Harold Urey of the University of Chicago, then 
at Columbia University. 

The neutron is a particle (possessing wave characteristics as do, 
apparently, all particles) whose mass is almost equal to that of the 
proton, or nucleus, of the simple hydrogen atom, but differs from it 
in having no electric charge. Discovery of the neutron made it clear 
that atomic nuclei are compounds of tightly bound protons and neu- 
trons. The word nucleon is now used as a generic term for either 
protons or neutrons, the constituent particles of every atomic nu- 
cleus. Thus the complete picture of the atom emerged, along lines al- 
ready indicated (see page 126) : a central nucleus which is a tight core 
of protons and neutrons is surrounded by electrons in a larger space. 
The chemical nature of the atom is determined by its atomic num- 
ber, Z, which is both the number of protons in the nucleus and the 
number of electrons outside the nucleus; the weight of the atom is 
given approximately by the number, called A, which represents the 
sum of the protons and neutrons in each nucleus. (The electrons are 
not counted in A because their weight is negligible.) 

The number of neutrons in the nucleus contributes to the over-all 
weight of the atom but has hardly any effect on the chemical prop- 
erties. So different kinds of atoms which have the same atomic num- 
ber but different atomic weights are said to be isotopes of the same 
element. The simplest example is that of hydrogen. Ordinary abun- 
dant hydrogen has Z = 1 and A = 1, that is, its nucleus is simply a pro- 
ton. The heavy kind, which Urey discovered in 1932, is nearly iden- 
tical chemically with ordinary hydrogen because its Z = 1; but for this 



136 What Is Science? 

isotope A = 2, indicating that its nucleus consists of a binary com- 
pound of one neutron and one proton. In still another kind of hy- 
drogen, called tritium, Z 1, but A =: 3, because its nucleus is a com- 
pound containing one proton and two neutrons. 

Chemists are accustomed to designate the different elements by 
symbols. Thus they write Li to represent one atom of lithium and 
Na to denote one atom of sodium. Physicists interested in nuclear 
work use the same symbol to designate an atom or a nucleus, usu- 
ally attaching the Z value as a subscript and the A value as a super- 
script. Thus they write LiJ for one atom of the particular isotope of 
Lithium (Z= 3) whose A is equal to 7. Such a nucleus has three 
protons and four (73) neutrons. 

In terms of this notation the reaction studied by Cockroft and 
Walton in their pioneer researches in 1932 would be written: 

Hi + Lil = He 2 4 + He! 

This means that some at least of the high speed protons on striking 
a lithium atom on the target in the proper way penetrate the nu- 
cleus, momentarily creating an unstable melange of four protons and 
four neutrons, which is just the stuff necessary to make two helium 
nuclei. These in turn group together and promptly fly apart. In such 
a violent process the electrons get knocked off, but later when the 
atoms produced come to rest they will manage to pick up some stray 
electrons and become normal neutral atoms again. 

Concurrently with these advances in nuclear physics, experimental 
means were developed for making precise measurements of the 
masses of the different kinds of atoms, using an instrument known 
as a mass spectrograph. This made possible the full quantitative 
verification of Einstein's 1905 prediction that mass and energy were 
equivalent. 

The operation of this instrument is rather neat. There are many 
kinds of mass spectrographs but all have in common a highly evacu- 
ated tube which can be placed partly between the poles of a magnet 
producing a uniform magnetic field. Figure 8 shows a schematic 
drawing of the type spectrograph developed by A. }. Dempster of the 
University of Chicago. An electric discharge in the ion source con- 



Physics 137 



Uniform magnetic field normal to paper 




Applied voltage 

i | ... ^ 

Photographic plate 



Fig. 8 Schematic diagram of one type of mass spectograph invented by 
Arthur /. Dempster of the University of Chicago. 

verts gas atoms into ions 11 which are then accelerated by applying a 
proper electric voltage between the two electrodes, each containing a 
slit, just above the ion source. The ions which have been thus ac- 
celerated then move in the main part of the vacuum tube in a mag- 
netic field which, in the diagram, is at right angles to the plane of the 
page. The action of the magnetic field causes the ions to travel in 
semi-circular paths, ions of larger mass moving in larger circles. By 
careful measurement of the radii of curvature of the paths, the ap- 
plied voltage, and the magnetic field strength, a precise determination 
can be made of the mass of the different ions. 

In the experiment in which pairs of helium nuclei are produced 
when hydrogen ions (protons) bombard lithium, the measured en- 
ergies of motion of the two helium ions are much greater than the 
0.5 million electron volts of energy of motion of the accelerated hy- 
drogen ions. In fact their energy measured 17.06 MEV (million 
electron volts). But it was also known from mass spectrograph work 
that the mass of two helium atoms is less than the sum of the mass 
of a hydrogen atom and of a lithium-7 atom. Here are the figures, 
expressed in units such that the abundant isotope of oxygen is arbi- 
trarily set exactly equal to 16: 

11 An ion is an atom either deficient in electrons or possessing more than its nor- 
mal share; in this state the atom is not electrically neutral, being either positively 
or negatively charged, depending on the defect or excess of electrons. 



138 What Is Science? 

Mass of Hi 1.00812 

Mass of Li 3 7 7.01822 



Sum 8.02634 

Mass of two HeS 8.00780 



Mass loss in reaction 0.01854 

According to Einstein's rule, one such unit of mass is equivalent to 
931 MEV and therefore this mass decrease must correspond to the 
release of 17.26 MEV, which checks with the observed energy of the 
helium ions (within the range of experimental uncertainty of meas- 
urement). 

In the early nineteen-thirties many atomic masses were very accu- 
rately measured and the energy of products of many nuclear reac- 
tions became known. Thanks to this work detailed and exact verifica- 
tion of Einstein's idea became commonplace. One of my most vivid 
memories is of a seminar at Princeton when a graduate student was 
reporting on researches of this kind and Einstein was in the audi- 
ence. Einstein had been so preoccupied with other studies that he 
had not realized that such confirmation of his early theories had be- 
come an everyday affair in the physical laboratory. He grinned like a 
small boy and kept saying over and over, "1st dass wirklich so?" Is it 
really true? as more and more specific evidence of his E = me 2 rela- 
tion was being presented. 

Now that literally hundreds of nuclear reactions have been exam- 
ined in great detail, a wealth of remarkable facts has been uncovered. 
It has been learned, for example, that some of the reactions go well 
only if the particles hit each other at the right relative speed. In gen- 
eral, the yield of such reactions goes up as the bombarding energy is 
increased, but in these cases a small increase in bombarding energy 
above the key value will greatly decrease the yield. This phenomenon 
is known as resonance and finds its theoretical explanation in the 
wave nature of the nuclear particles, according to ideas developed by 
Gregory Breit of Yale University and Eugene Wigner of Princeton. 

Although reactions with lighter elements can be made to go with 
machines producing voltages of less than a million, more powerful 
equipment is needed for study of analogous reactions in the heavier 



Physics 1 39 

elements. That is because the greater electrical charges on their nu- 
clei produce stronger forces of repulsion. The discoveries about the 
lighter elements acted as a compelling stimulus to the building of 
such machines. The cyclotron, invented by Ernest Lawrence, of the 
University of California, is the best known. 

An important by-product of this work was the discovery that many 
nuclear reactions produce unstable isotopes whose instability mani- 
fests itself in radioactivity. In this way it is possible to produce small 
quantities of a radioactive isotope of nearly every chemical element 
and these have become important tools for study of chemistry. 

In the Cockroft-Walton bombardment of lithium by hydrogen, 
more energy is given off in the resulting helium, as we have noted, 
than was in the original proton, but this source of energy has no 
practical significance: no way is known to aim the accelerated pro- 
tons so that every one of them makes a direct hit on a lithium nu- 
cleus. The vast majority of the nuclear bullets fail to score and there- 
fore there is no over-all gain in energy in such an apparatus, even 
though there is a large gain in the case of the particular protons that 
make the right kind of hit. 

But in 1938 in Berlin Otto Hahn and Lise Meitner made a fateful 
discovery of a new kind of nuclear reaction which releases enormous 
quantities of energy. When they allowed a beam of neutrons to fall 
on a uranium compound, they found in the resulting material a large 
variety of radioactive isotopes of chemical elements having about half 
the atomic weight of the original uranium. From this they inferred 
that the uranium atoms captured some of the incident neutrons and 
became highly unstable, splitting apart into roughly equal fragments. 
Uranium consists principally of two isotopes, A 238 and A 235, 
so the fragments would be atoms in the general range A 100 to 
130. From the known masses it was at once evident that the frag- 
ments would have a great deal more energy than the original ura- 
nium atom and the neutron which struck it. Later experiments 
showed that the energy release was about 200 MEV for each ura- 
nium atom split. 

The process was called fission. It began to be intensively studied 
for its fundamental interest in several laboratories and soon it was 
discovered that, besides the larger fragments, several neutrons were 



140 What Is Science? 

released for each uranium atom split. These in turn could split more 
uranium atoms, releasing more neutrons, and so on, giving the pos- 
sibility of a violent explosion. The result is the atomic bomb, now 
part of the armament of several nations. When such reactions are 
suitably controlled they will also release energy in forms that can be 
used to generate electric power. 

Other developments in the theory of light elements showed that 
reactions which build elements like carbon and oxygen from hydro- 
gen are the primary source of the energy given off by the sun and 
other stars. Details of this grand synthesis were worked out by Hans 
Bethe of Cornell. Recently some of the same ideas have been used to 
produce military weapons of much greater power (equivalent to 
more than ten million tons of TNT) than the atomic bombs based 
on uranium fission. 

The program which today occupies nuclear physicists consists in 
part of filling in gaps of knowledge in familiar areas, in part of com- 
ing to grips with new fundamental problems. A major task is to de- 
termine exactly all the properties of atomic nuclei not merely their 
masses but also their magnetic strength and their behavior in regard 
to emission of gamma rays and in various transmutation reactions. 
Another question of the first importance centers on the nature of the 
forces which hold nucleons together in a complex nucleus. It is rec- 
ognized that these forces are not like any previously known. They 
are not electromagnetic or gravitational, but of a specifically new 
kind. 

Nucleons, as I have indicated, consist of protons positively 
charged particles and neutrons possessing no electric charge. The 
protons repel each other because they have like charges, and the neu- 
trons are unaffected by electrical forces. Yet despite this electrical 
arrangement which should result in disintegration of the nucleus, the 
particles are in fact very tightly bound together. One infers, there- 
fore, that there are strong cohesive forces at work in a nucleus, which 
are not electrical in character, at least not in the ordinary sense. That 
is, while they may be related to electromagnetic effects, they do not 
manifest themselves as do the usual repulsions and attractions be- 
tween charges, varying as the inverse square of the distance between 
them. It has been observed that these forces are especially strong in 



Physics 141 

binding together a pair of protons and a pair of neutrons to make the 
very stable alpha particle or nucleus of the helium atom. And it is 
known also that the forces are "short-range" in effect: although they 
are very strong when the interacting particles are within a distance 
of 10~ 12 cm (or less) of each other, they become negligibly weak out- 
side this range, so that the nucleons in a large nucleus exert strong 
forces on their nearest neighbors but do not appreciably affect the 
nucleons on the other side of the nucleus. The exact mathematical 
law of the dependence of the forces on the distance between the in- 
teracting particles is not known. These are among the matters being 
studied energetically in laboratories all over the world. 



Besides the electrons, protons and neutrons of ordinary matter, 
other kinds of particles have been discovered which have transient 
existences in our laboratory apparatus. 

First there is the "neutrino/' an affectionately diminutive Italian 
word which means little neutron. The evidence for its existence is 
far from being as complete or convincing as one would like. 

Some radioactive atoms are called beta-emitters. They emit a high 
speed electron from the nucleus when they undergo transformation 
into the next higher element. As we do not think there are any elec- 
trons in the nucleus, we must suppose that a neutron changes itself 
into a proton and an electron in this process. 

Both before and after transformation the atoms involved seem to 
be all alike, in respect of their mass which is a measure of their total 
energy content. Now according to the principle of conservation of 
energy the difference in energy of the initial atom minus that of the 
final atom ought to be the energy observed to be carried off by the 
emitted particle. But the remarkable thing is that the emitted elec- 
trons do not all come out with this same definite amount of energy, 
but show a wide statistical spread in their energies of motion. One 
supposes therefore that there were really two particles emitted in each 
spontaneous disintegration of this type and that the total available 
energy is divided between them in different ways in different spe- 
cific instances of disintegration. One of these particles is the observed 
electron and the other is the hypothetical unobserved neutrino. It 



142 What Is Science? 

is postulated that the neutrino has the necessary properties to account 
for the strange fact that it is able to penetrate the walls of the appara- 
tus and escape detection: that is, that it has no electric charge and no 
mass. Thus the neutrino, if it can be said to exist, reveals itself by the 
absence elsewhere (in the electron) of the energy it is supposed to 
have appropriated rather than by any direct evidence of its presence. 
We know it exists in the same way that we know of the existence of 
burglars who are successful but not caught. 

Second, there is the positron. This particle is like the electron, but 
positively charged. It has only a transient existence, for when a 
positron collides squarely with an electron they mutually annihilate 
each other, the total energy which is inherent in their mass being 
transformed into two quanta of high energy X rays. Alternatively, if 
the positron collides with an electron that is attached to an atomic 
nucleus, the electron and positron may annihilate each other with the 
emission of only one gamma ray quantum, the momentum of recoil 
being taken up by the atomic nucleus. 

The energy needed to bring a positron into existence is about 
500 kev. (One kev. is the energy gained by an electron on falling 
freely through a potential difference of one kilovolt.) There is no 
evidence that electric charge can be made from nothing, so when a 
positron is created, an electron must be created at the same time; thus 
the total charge involved in the created electron-positron pair is 
zero. 12 The total energy needed to generate such a pair is about one 
million electron volts or 1,000 kev. 

"Perhaps an additional word of clarification is needed on this point. Electric 
charges of opposite tendency are by convention called either positive or negative. 
This convention is then elaborated in mathematical treatment. The advantage of 
representing opposite charges by numbers of opposite algebraic sign is easily under- 
stood. For with this method the force between two charged bodies can in all cases 
be written as proportional to the product of the individual charges. Thus the fact 
that like charges, whether positive or negative, repel each other with a force pro- 
portional to their product, is conveniently expressed in the algebraic rule that the 
product of two numbers of like sign is positive. No processes have ever been ob- 
served in which there is a change in the total algebraic amount of electric charge 
present. This is to say that electric charge can neither be created nor destroyed. If 
an electron is created by some physical action, it is always accompanied by a 
counterbalancing positron, of equal and opposite charge, so that the net result 
is to leave unchanged the algebraic balance sheet, or, in physical terms, the net 
amount of electric charge in the world. 



Physics 143 

Positron and electron pairs are generated as one of the processes 
which occur when X rays having quantum energies in excess of one 
million electron volts go through matter. Likewise, when high energy 
electrons go through matter they may interact with nuclei in such a 
way that positron-electron pairs are created by materialization of 
some of the incident electrons' energy of motion. 

Positrons were discovered in cosmic rays by Carl Anderson at 
Pasadena in 1932. Since then a great deal has been learned ex- 
perimentally and theoretically about the details of their generation 
and annihilation. These processes afford the first direct experimental 
evidence that the total number of particles of each kind in the uni- 
verse is not constant except in the case of light quanta, which are 
believed to be created and destroyed in the light-emitting and absorb- 
ing process. 

Third, there are mesons. Several kinds of these particles are found, 
some positive, some negative and some neutral, and having various 
masses of the order of two hundred times the mass of the electron and 
therefore about one-tenth the mass of the proton. The name meson 
was chosen to indicate their intermediate character with regard to 
mass between electrons and protons. 

Mesons occur in cosmic rays, being produced in the upper atmos- 
phere by high-energy particles from interstellar space which make 
up the primary beam of cosmic ray particles. Mesons transform spon- 
taneously into each other with emission of gamma rays in a com- 
plicated series of processes which is not yet fully worked out. 

With the construction of high-energy particle accelerators giving 
particle energies in excess of 300 million electron volts, it has been 
possible to produce mesons in the laboratory in far larger quantities 
than occur in cosmic rays, so that knowledge of their properties is 
now being accumulated at a rapid rate. 

The existence of mesons was first postulated on theoretical grounds 
by H. Yukawa in Japan in 1935, before their discovery in cosmic rays. 
Yukawa suggested their existence to explain certain features of the 
forces between protons and neutrons, and they are today believed 
to play an important role in that way. But our knowledge of the rela- 
tion between free mesons, and those which may play such a role in- 
side stable nuclei is still quite meager. 



144 What Is Science? 

I have devoted a large part of this essay to nuclear research because 
in recent years it has been the major field of interest in fundamental 
physics. But it would be wrong to suppose that all progress in that 
science has been confined to one branch. On every front work has 
been done to improve our understanding and control over the prop- 
erties of matter. The fascinating phenomenon known as supercon- 
ductivity has been intensively studied. Superconductivity is a prop- 
erty of certain metals whereby they lose all their electrical resistance 
at very low temperatures, so that currents induced in them seem to 
flow indefinitely; at the same time the metals in this state become al- 
most impermeable with respect to magnetic forces. Technical devices 
of great importance have been devised among them the means of 
generating elecric waves of a few centimeters' wave length, and the 
electron microscope for seeing detail much finer than is possible with 
light. 

Beyond X-ray diffraction and electron diffraction, physicists have 
developed the technique of using diffraction of a beam of neutrons 
falling on a crystal as another powerful tool for studying how atoms 
are arranged in crystals and in molecules. Radioactive by-products 
from uranium reactors have been perfected as tools of research in 
chemistry and biochemistry and radiations from such man-made 
sources are being used in cancer therapy. 

A vast amount of progress has been made, and a vast amount more 
remains to be made. There was probably never such an exciting 
period in the history of the science. Physics today is lavishly sup- 
ported because of the military importance of many of its findings. It 
has suddenly become a popular science, an object of national interest 
and concern. This official solicitude has created a host of difficulties, 
some intruding harshly into the lives of scientific workers, some af- 
fecting the very course of research. Not a few scientists, especially in 
the United States, are concerned lest huge government grants and con- 
tracts distort the direction and emphasis of studies in physics. At 
any rate it is clear that physics in the near future will run out of 
neither problems nor money. 



Physics 145 



Summary of the Particles of Atomic Physics 



The important particles of atomic physics are summarized below for 
convenient reference. The mass of the particle is given in units of the 
electron mass which is 9.107 x l(h 28 gram. The charge is given relative 
to the magnitude of the electron charge which is 1.602xl(H 9 cou- 
lomb. 

The mass-energy relation of Einstein, E = me 2 , is conveniently ex- 
pressed in laboratory units by expressing the energy in million elec- 
tron volts (MEV), one MEV being the amount of energy acquired 
by an electron on falling freely across a potential drop of one million 
volts. The energy equivalent of the mass of one electron is then 
0.511 MEV. Atomic masses are usually expressed on a scale of atomic 
mass units (amu) in which the mass of the ordinary oxygen atom is 
arbitrarily assigned the value 16. The energy equivalent of 1 amu 
corresponds to 931.04 MEV. 

Photon or Light Quantum (Mass, 0; Charge, 0) 

These names are used interchangeably to emphasize the corpuscu- 
lar character of light and X rays and gamma rays. The quantum idea 
was first introduced by Max Planck in 1900 and extended by Albert 
Einstein in 1905. 

The energy of a quantum is proportional to the frequency of the 
light or inversely proportional to its wave length. Quanta of red light 
correspond to two electron volts and of violet light to four electron 
volts. X-ray quanta as used in radiography correspond to 30,000 to 
50,000 electron volts. For X-ray therapy energies up to several million 
electron volts find application. Gamma rays are the same physically as 
X rays. The term gamma ray usually connotes that the radiation was 
emitted in a nuclear process or in positron-electron annihilation. 

Electron (Mass, 1; Charge, 1) 

Name suggested in 1891 by G. Johnstone Stoney. Ratio of charge 
to mass measured in 1897 by J. J. Thomson. Charge measured in 
1909 by R. A. Millikan. 

Electrons make up the parts of atoms outside the central nucleus. 



146 "What Is Science? 

An atom containing Z electrons is said to have an atomic number of 
Z which ranges for naturally occurring elements from Z 1 for hy- 
drogen to 2 = 92 for uranium. The chemical properties of the 
atom are determined by Z so each chemical element corresponds to 
a different value of Z. 

Positron (Mass, 1; Charge, + 1) 

Same mass as electron but positively charged. Existence was 
predicted theoretically by P. A. M. Dirac in 1930. Positrons were dis- 
covered experimentally by Carl Anderson in 1932. Positrons do not 
exist in normal matter. In certain collisions involving high-energy 
particles and high-energy gamma rays, pairs (that is, one electron 
and one positron) are created or materialized, their mass being cre- 
ated from the mass equivalence of part of the energy of impact. The 
positrons so formed have only a transient existence being later an- 
nihilated in collision with electrons, their energy and that of the an- 
nihilated electron being given off as gamma rays. 

Nucleon 

This is a generic term referring to either a proton or a neutron. 
The nucleus of an atom of atomic number Z contains Z protons to- 
gether with N neutrons, where Z + N = A. A is the total number of 
particles in the nucleus, and is therefore the integer closest to the 
atomic weight of the atom on the usual scale. Except for hydrogen, 
A is always equal to or greater than 2Z. 

Proton (Mass, 1836.5; Charge, + 1) 

The proton is the nucleus of the atom of ordinary hydrogen and 
is the electrically charged constituent of all nuclei. The proton was 
"discovered" gradually during the 1890s with the evolution of ideas 
concerning electrical conduction in gases. 

Neutron (Mass, 1839; Charge, 0) 

The neutron carries no charge and has a mass slightly in excess of 
that of the proton. Neutrons are apparently stable when bound in 
atomic nuclei. Free neutrons however are radioactive and transform 



Physics 147 

spontaneously into protons, electrons and neutrinos, with an average 
life of about 13 minutes. In terms of atomic mass units, 

Neutron 1.008982 
Proton + electron 1 .008142 



Difference 0.000840 

The mass difference is equivalent to an energy of 0.782 MEV which 
appears as energy of motion of the proton, electron and neutrino in 
the spontaneous disintegration of the free neutron. 

The neutron was discovered by James Chadwick in 1932. 

Neutrino (Mass, 0?; Charge, 0) 

The neutrino is a hypothetical particle, not directly observed, 
which has been supposed to be emitted in radioactive processes in 
which electrons or positrons are also emitted. Such radioactive proc- 
esses are called beta-processes, the simplest example being that of 
the spontaneous radioactive decay of the free neutron. First suggested 
by Wolfgang Pauli and developed into theory of beta-decay by En- 
rico Fermi in 1934. 

Deuteron (Mass, 3671.2; Charge, + 1) 

The dcuteron is the simplest compound nucleus, consisting of a 
binary compound of one proton and one neutron. It is the nucleus 
of the heavy form of hydrogen known as deuterium which was dis- 
covered by Harold Urey in 1932. Its mass is less than the sum of the 
mass of the proton and the neutron by about 4.4 units. This is the 
mass equivalence of the energy released when one deuteron is formed 
by the union of one proton and one neutron. Because of the strong 
binding energy of the proton and the neutron, the energy of a deu- 
terium atom is less than the sum of the energies of a proton, a neu- 
tron and an electron, separate and at relative rest, and therefore 
deuterium is stable with regard to radioactive decay. 

Alpha Particle 

This is the historic name given to the heavy particles emitted in 
the radioactive decay of heavy elements such as uranium, thorium, 



148 What 1$ Science? 

radium and others. An alpha particle is the nucleus of the helium 
atom and consists of a very stable compound of two protons and two 
neutrons. The energy released on formation of one alpha particle 
from two neutrons and two protons is 28 MEV. 

Meson 

A generic name for a class of particles originally discovered in 
cosmic radiation, but which have also been produced artificially by 
bombardment of targets with particles accelerated to several hundred 
million volts in modern high-energy particle accelerators. Mesons are 
of various types, both charged and uncharged, and have masses of the 
general order of several hundred electron masses. The full story on 
these particles is not yet known and is the subject of vigorous ex- 
perimental investigation in laboratories throughout the world. Exist- 
ence of mesons was first predicted theoretically in 1935 by H. Yukawa 
in Japan. 

Pions or v mesons. (Mass, 280 10; Charge, 1) 

These mesons are of two kinds, positively and negatively charged. 
They were first recognized in cosmic radiation by C. M. G. Lattes in 
1947, and first generated artificially in the laboratory in 1948 by E. 
Gardner and C. M. G. Lattes using a beam of alpha particles of 
360 MEV energy from the 184-inch synchro-cyclotron at the Uni- 
versity of California. Pions have a mean life of 0.9 x 10~ 8 sec. before 
decaying spontaneously into a charged muon and a neutral particle 
of uncertain nature. Those occurring in cosmic rays are produced in 
the upper atmosphere by collision of high speed protons and neutrons 
from outer space with the atoms of the atmosphere. 

Muons or p. mesons. (Mass, 215 : 2; Charge, : 1) 

These mesons were first discovered in cosmic radiation by C. D. 
Anderson and S. Neddermeyer and also by J. C. Street and E. C. 
Stevenson in 1937. Later they were recognized to be the products of 
decay of the pions. The muons in turn decay spontaneously into high 
energy electrons (maximum energy about 55 MEV) and neutral 
particles of uncertain nature, having a mean life before decay of 



Physics 149 

2.15xlO- 6 sec., more than two hundred times greater than that of 
the pion. 

Neutretto 

A name sometimes used to refer to hypothetical mesons without 
electric charge. 

Hyperon 

A generic designation of particles heavier in mass than the proton, 
which can decay spontaneously into nucleons and pions. Intensive 
cosmic ray research is at present revealing a vast range of complicated 
phenomena seemingly involving a number of additional kinds of 
particles of masses greater than that of the pion which undergo vari- 
ous kinds of spontaneous transmutations not as yet fully understood. 

Anti-proton 

A hypothetical particle of mass equal essentially to that of the 
proton but having unit negative charge instead of unit positive 
charge. 



CHEMISTRY 

JOHN READ 



about 

John Read 



John Read was born February 17, 1884, in the English west country. 
He was educated in Somerset and at Finsbury Technical College, 
London. After completing his college course he enrolled at the Univer- 
sity of Zurich, where he followed research in chemistry and took his 
doctorate under Alfred Werner, distinguished for his contributions to 
stereochemistry and the study of complex inorganic compounds. For 
eight years, beginning in 1908, Read conducted joint researches with 
W. J. Pope who held the chair of chemistry at Cambridge; in 1916, 
as a result of the reputation gained in this work, he was appointed 
professor of organic chemistry in the University of Sydney, Australia, 
where he worked extensively on the chemistry of Australian, plant 
products. He returned to Britain in 1923 to become professor of 
chemistry and director of the chemistry research laboratory in the 
United College of St. Salvator and St. Leonard, University of St. 
Andrews, Scotland. 

The author of many outstanding papers in the fields of organic and 
stereochemistry, Professor Read is equally well known for his books 
on alchemy and the history of chemistry. Among his best kno\m 
writings addressed to a general audience are Prelude to Chemistry, 
(N.Y., 1937); Humor and Humanism in Chemistry, (London, 1947); 
The Alchemist in Life, Literature and Art, (London and Edinburgh, 
1947). 

A Direct Entry to Organic Chemistry (1948), a popularization 



about John Read 153 

of this rather difficult subject, won for Read the newly inaugurated 
Cortina-European prize of a million lire in 1949, as "the best book 
on popular physical science published in any language within the 
preceding five years." Since its publication Read has lectured exten- 
sively in Italy and other European countries, and in 1953 was ap- 
pointed by the British government as one of the five British mem- 
bers of an Anglo-Italian cultural commission. 

Read has long been interested in the region of his birth. He 
visited Thomas Hardy frequently at his home in Dorchester; he likes 
to walk through the Wessex countryside making friends with the 
farm folk, observing the local customs, recording the folk speech, 
stories and beliefs. He has written books and plays and given dialect 
broadcasts about this part of England. He has also written a history 
of the city of St. Andrews and its university. His numerous academic 
distinctions include Fellowship of the Royal Society since 1935 and 
the presidency of the chemical section of the British Association for 
the Advancement of Science in 1948. He is married and has two sons, 
one of whom, Arthur Hinton Read, is a mathematician and author 
of an attractive popular book, A Signpost to Mathematics. 



CHEMISTRY 

JOHN READ 



Owing to its vast extent, natural science has been divided, both on 
practical and intellectual grounds, into the physical sciences, such as 
chemistry, physics and geology, and the biological sciences, such as 
botany, zoology and physiology. Nature, however, has an essential 
unity; so that the various branches of science are interdependent and 
possessed of no rigid boundaries. 

Chemistry is a branch of science which deals with the study of mat- 
ter, or in other words with the character of the "stuff" of which the 
material universe is composed. It is obvious to the senses that matter 
abounds around us in many kinds and forms. It is the task of chem- 
istry to separate from this heterogeneous assemblage of matter, va- 
rious homogeneous portions known as substances, each of which has 
its individual composition and properties. A vast mass of information 
of this kind has been accumulated as a result of patient experiments 
and observations. The observed characters and interrelationships 
have led to many consequences, notably to the classification of 
substances, to the preparation of one known substance from another, 
and to the elaboration of new substances unknown in nature. Pro- 
longed work of this kind was necessary before any accurate idea could 
be formed of the proximate or ultimate nature of matter. In the mod- 
ern development of chemistry, facts, accurately established by experi- 
ment, led to the formulation of generalized statements, or laws. Cer- 
tain laws, fitted by imaginative processes of thought into a wider 



Chemistry 155 

conception, gave birth to hypotheses, which when fully established 
took higher rank as theories. Theories are thus conclusions drawn from 
accumulated facts and capable of leading to the prediction of new 
facts. 

In tracing the origin and development of chemical knowledge it 
must be emphasized that chemistry is based fundamentally upon very 
obscure principles, which were brought to light only after the lapse 
of long ages of preliminary speculation and arbitrary experiment. Al- 
though probably the most obscure, chemistry is certainly the most 
romantic of all the branches of science. The history of its develop- 
ment stretches back through a thousand years of alchemy into the 
misty prehistory of primitive superstitions and religions. Primi- 
tive man, in a rough and ready way, must have paid attention to the 
various materials around him and have adapted them to various uses; 
herein we discern the dawn of pure and applied chemistry. 

The ancient civilizations of the Middle East, in the course of un- 
numbered centuries, developed a knowledge of various metals and 
alloys, and of methods of making and using fermented liquors, 
soap, glass, stoneware, leather, alum, and many other materi- 
als. They had, however, no knowledge of what we now call chemistry, 
although the dawn of imaginative ideas may be seen in the Chaldean 
association of the known planets and metals "the bodyes sevene eek" 
as Chaucer called them much later with human organs and indi- 
vidual destinies. 

At this point, in order to get a clearer notion of early views of the 
cosmos, it may be mentioned that until the time of Descartes, in the 
seventeenth century, matter and mind were not regarded as mutually 
exclusive. That is a modern view. In ancient and medieval times, 
gross or tangible matter was supposed to shade away through increas- 
ingly subtle grades of matter, like mists, smokes, exhalations, and air, 
to ether, animal spirits, the soul, and spiritual beings, all forming 
links in an essential unity. 

The earliest imaginative idea of physical science which may be dig- 
nified by the title of a "theory" was that of the four qualities and the 
"four elements/' usually ascribed to Aristotle but traceable in Egypt 
and India as far back as 1 500 B.C. This theory, held so widely in one 
form or another by many civilizations over a long period, bears out 



156 What Is Science? 

the statement that "there is a great oneness in the human mind in the 
matter of broad principle in crude cosmical ideas/' The theory has 
often been represented diagrammatically in some such form as that 
given below (Fig. 1): 

FIRE 




EARTH 



According to this theory, all matter is composed of the four so- 
called "elements," earth, air, fire and water. Each element, in turn, 
is pictured as a material embodiment of pairs of fundamental qual- 
ities: the hot, the dry, the cold, and the wet. This primitive theory is 
not to be scorned: the "elements" were selected with discrimination, 
and the scheme summarizes a great deal of observation and reflec- 
tion. At an early stage in his intellectual development, man must have 
been led to discriminate between what we now call the three states 
of aggregation of matter: the solid, liquid, and gaseous, here repre- 
sented by earth, water, and air. The fourth "element," fire, stood for 
what we now term heat or energy. 

Let us look into this conception a little further. Water is cold and 
wet. Heat water and replace the cold quality by the hot one, and the 
result is a change of water into steam, that is, into a vapor or "air." 
One "element" has thus changed into another, or undergone trans- 
mutation, to use an alchemical term. The fundamental alchemical 
idea of transmutation is thus implicit in the theory. Nowadays, of 
course, the process is viewed simply as a change of liquid water through 
the absorption of heat, or energy, into the gaseous form of the same 
substance and there is no question of transmutation. 



Chemistry 157 

This ancient theory may be traced back to a still more primitive 
mode of thinking, known as the "Doctrine of the Two Contraries," 
dependent upon the recognition of a distinction between pairs of op- 
posites, such as cold and hot, dry and wet. An apposition of primary 
importance in alchemy was that of the two opposed, or contrary, "ele- 
ments" fire and water. 

So we come to alchemy, the immediate precursor of chemistry. Al- 
chemy was a long-lived ancestor, for it lasted for more than a millen- 
nium, from at least early Christian times until the end of the seven- 
teenth century. Alchemy was not merely rudimentary chemistry. It 
was a vast network of this incipient science, interwoven with astrology, 
philosophy, religion, mysticism, theosophy, magic, and many other 
strands. Its tenets made a great appeal to the human mind; so much 
so that the authoritative opinion has been expressed in recent years 
that alchemy is no less important in the study of psychology than in 
that of chemistry. But alchemy has been outmoded for more than two 
centuries; and so there is little realization at the present day of the 
extent to which alchemical conceptions and imagery permeated the 
thought and also the art of the Middle Ages. 

No definite statement can be made concerning the origin of al- 
chemy; but there is little doubt that alchemical knowledge and ideas 
were gathered from the ancient civilizations of Egypt, Babylonia, In- 
dia and China. From Greece, Syria and Persia this accumulated 
corpus of alchemy was transmitted to Islam. Eventually the accumu- 
lated knowledge of the Moslem alchemists, drawn from these 
various sources and augmented in its passage through Islam, was 
brought into western Europe, chiefly through Spain. 

The main tenets of alchemy were, first, that all forms of matter are 
one in origin; secondly, that these forms are produced by evolutionary 
processes; thirdly, that matter has a common soul which alone is per- 
manent, the body or outward form being transitory and capable of 
undergoing transmutation, or change into a different outward form. 
Essentially, these views are very similar to those of modern physical 
science; for in this twentieth century "modern alchemy," as Lord Ruth- 
erford called it, has achieved many transmutations of the elements of 
modern science, formerly supposed to be immutable. 

In the deductive philosophy of ancient Greece the idea first came 



158 What Is Science? 

to birth that imaginative thought could lead to the deduction of 
truths from considerations of general principles. Alchemical reasoning 
and ideas were derived in large measure from Greece; so it is not sur- 
prising that alchemical reasoning was mainly deductive and based to 
a great extent on two a priori assumptions. These were, first, the unity 
of matter; secondly, the existence of a potent transmuting agent, 
known as the philosopher's stone. From the postulate of the essential 
unity of all things it followed that this medicine of the metals became 
also the medicine of man. In this guise the philosopher's stone was 
known as the elixir vitae, or elixir of life. 

Herein may be discerned the powerful incentive which actuated 
the strenuous, costly and often unpleasant labors of some forty gen- 
erations of alchemists. "Gold," wrote Goethe, "gives power; without 
health there is no enjoyment, and longevity here takes the place of 
immortality/' And, as Liebig observed: "In order to know that the 
philosopher's stone did not really exist, it was indispensable that ev- 
ery substance accessible should be observed and examined ... in 
this we perceive the almost miraculous influence of the idea." 

The alchemists themselves ranged from impostors and charlatans 
having no real claim to the title, through uninstructed "puffers" (Fig. 
2) and would-be goldmakers, to skilled practicants, scholastic phi- 
losophers, adepts, and religious mystics. To the higher type of alche- 
mist, alchemy was much more than an experimental science. It was a 
grandiose philosophical system. In their own eyes, the efforts made by 
the adepts and religious mystics to transmute metals were attempts to 
prove the truth of the broad philosophical system of alchemy by 
means of material experiments. 

Now, to follow along the chemical strand of the alchemical web, 
the two opposed "elements," fire and water, came to light in a new 
form in the "sulphur-mercury theory" of the metals, which seems to 
have been propounded by the Moslem alchemists possibly in the 
eighth century A.D. The sulphur and mercury of this theory were not 
the tangible substances bearing these names. They were abstract 
""principles," sulphur being essentially a principle conferring upon 
combustible bodies the ability to burn; while mercury denoted the 
mineral spirit of metals and also the property of liquidity or fusi- 



Chemistry 159 




Fig. 2 A "Puffer" and his assistant. Hans Weiditz, 1520. 

bility. Essentially these imagined principles constituted a new view 
of the fire and water of Aristotle's four elements. 

According to this conception the medieval alchemists considered 
that when these two natural principles came together under plane- 
tary influences in the bowels of the earth they gave rise to the perfect 
metal, gold; if they were slightly impure they gave silver; if they were 
markedly impure they furnished base metals, such as tin and lead. 
If, however, the two principles could be brought together in states of 
superfine purity, they could yield something so much purer than 
ordinary gold that a small amount of this product (the philosopher's 
stone) would be able to transmute a very large quantity of a base 
metal into gold of ordinary purity. 

This was the idea which animated generation after generation of 
alchemists throughout the medieval period, and even down to the 
days of Boyle and Newton. The chief task of the alchemical adept 
was to imitate, and even surpass, nature in bringing about such 
changes. After all, that is a leading motive of modern chemistry. Also 
in modern parlance it would be correct to call the philosopher's stone 
a catalyst. Here again the alchemists are vindicated; for what more po- 



160 What Is Science? 

tent catalyst could be imagined than the neutrons which start and 
propagate the explosive transmutation of uranium 235 into other ele- 
ments? "Everything possible to be believ'd," wrote the English poet 
and mystic, William Blake, "is an image of truth. What is now proved 
was once only imagined." 

Beyond chance discoveries of new substances and processes and 
the development of various kinds of apparatus, alchemy had little to 
show in the way of advance until early in the sixteenth century when 
Paracelsus gave a new direction to operative alchemy and greatly en- 
larged its scope by allying it with medicine. Paracelsus (1493-1541) 
was a Swiss propagandist of a new order, both in alchemy and medi- 
cine, and he lashed the physicians of his day with a merciless tongue 
and pen. The true goal of alchemy, he insisted, must be to prepare 
medicines instead of seeking gold. The ensuing period of "iatrochem- 
istry," spagyric chemistry, or chemistry applied to medicine, lasted into 
the eighteenth century. Meanwhile the old alchemy persisted, but 
slowly declined. Paracelsus modified the ancient sulphur-mercury the- 
ory by introducing a third principle which he termed salt. In this 
system of the tria prima, or three hypostatical principles, often shown 
symbolically by a triangle (Fig. 3), the names sulphur, mercury, and 
salt had both a chemical and a mystical significance. Chemically 
they stood for inflammability, metallicity, and fixidity; mystically, for 
the soul, spirit, and body of man. 

In medicine, the herbalist of the ancient Galenic order now be- 
came a pharmacist, or compounder of chemical medicines. The end 
of the seventeenth century found iatrochemistry on the wane; but, 
during this period of transition the iatrochemists, despite certain ex- 
cesses, had promoted the steady growth and diffusion of chemical 
knowledge and laboratory practice. The gradual change from alchemy 
to chemistry became evident in a notable succession of early text- 
books of chemistry published in the seventeenth century and cul- 
minating in Lemery's celebrated Cours de Chymie (1675). Lemery 
(1645-1715) practised as an apothecary in Paris and gave some of the 
earliest public lectures and demonstrations in chemistry. His book, 
severely practical and completely devoid of the cryptic expression 
and mysticism of alchemy, achieved an unprecedented popularity in 
several languages, and did more to bring chemistry to the popular 



Chemistry 161 




Fig. 3 An alchemical emblem. 

notice than any other work published before the birth of modern 
chemistry at the end of the eighteenth century. This same century pro- 
duced, in the person of Glauber (1604-1670), the son of a Karlstadt 
barber, a true research chemist, whose discoveries and writings ex- 
erted a widespread and stimulating effect upon the incipient science. 
He died in poverty, leaving it on record that "by all that ever I writ 
I never gained one half-peny." 

Attention must now be turned from these practical empiricists to 
contemporary thinkers and men of ideas. In so doing we are faced 
with the question: Why did the scientific revolution of the seven- 
teenth century fail to reach chemistry? Looking back, we can now see 
that before chemistry could divest itself of the accretions of alchemy 
there were certain outstanding problems to be solved. Chief among 
them were: (1) the nature of a chemical element; (2) the nature of 
chemical change, especially of burning or combustion, and of the so- 
called "element," fire; (3) the chemical nature of the so-called "ele- 
ments," air and water. It is a great tribute to the Aristotelian scheme 
that three of its "elements" figure in this list of obstacles that blocked 
a break-through from alchemy to chemistry in the eighteenth century 
more than 3,000 years after the idea of the four elements was con- 
ceived in India and Egypt. 



162 What Is Science? 

These issues could not be resolved by processes of pure thought. 
They called for the application of systematic experiments logi- 
cal questions put to nature followed by accurate observation and 
intelligent interpretation. That is the scientific method in a nutshell. 

It is sometimes held that the publication of The Sceptical Chymist 
by Boyle in 1661 heralded the end of alchemy. The Hon. Robert 
Boyle (1627-1691), whom a schoolboy aptly described as "The Fa- 
ther of Chemistry and the Uncle of the Earl of Cork/' was a ver- 
satile worker in physics, "a great Lover of Chymical Experiments," and 
a man of singular beauty of character. It is true that in his famous 
book Boyle assailed vigorously the systems of the four elements and 
the tria prima, and put forward the modern idea of a chemical element 
as a body which cannot be resolved into simpler bodies. But the 
emergence of modern chemistry had to wait for more than another 
century. 

Why was the nature of combustion so important? . . . Because it 
is the most spectacular and fundamental of all familiar chemical proc- 
esses. Notice also that it involves all four of Aristotle's elements. A 
piece of wood burns: air is necessary; fire is manifest; water is an im- 
portant product of the burning; earth (ash) is left. Also, we must 
not overlook the literally "vital" importance of combustion; for it is 
a slow and regulated combustion that maintains animal heat in the 
metabolic processes upon which life depends. 

That great scientific, experimental and mechanical genius, Hooke 
(1635-1703), one-time assistant to Boyle, got very near to the core of 
the problem when he stated in his Micrographia (1665) that burning 
is due to "a substance inherent, and mixt with the Air, that is like, if 
not the very same, with that which is fixt in Salt-peter." His penetrat- 
ing remarks on combustion occur as a kind of aside in this first major 
work illustrating microscopical objects, and containing plates beau- 
tifully engraved by Hooke himself. Hooke's contemporary, Mayow 
(1641-1679), a brilliant but short-lived English physician, confirmed 
and emphasized earlier observations showing that air contracts in com- 
bustion and that the residual air cannot support combustion (or res- 
piration ) . 

Why did the nature of burning remain unsolved for another cen- 
tury? . . . Because Boyle, Hooke, and Mayow knew little of methods 



Chemistry 163 

of isolating or handling gases; consequently, they held no clues to the 
composition of air, fixed air (carbon dioxide), or water. And while 
air is "the food of fire," as the alchemists realized, fixed air and water 
are the products of combustion of all organic materials. 

It was essentially lack of knowledge of gases and of the experimental 
technique of handling them that gave a wrong direction to chemical 
theory when Stahl (1660-1734), professor of medicine at Halle, Prus- 
sian councilor, and royal physician, attributed combustibility to the 
presence in the combustible body of a constituent which he called 
"phlogiston" (1702). Burning was thus equivalent to a loss of phlo- 
giston, and a metal was regarded as a compound of its calx (oxide) 
with phlogiston. It was therefore held that loss of weight occurred in 
the burning of metals, just as it seemed to occur (because the gaseous 
products could not be collected and weighed) in the burning of a 
piece of wood or a candle. This view was held in spite of experimental 
evidence that tin and other metals increase in weight when heated in 
air, and that air contracts when bodies are burnt in it. It is fatal in 
science to close one's eyes to established facts. 

All the same, here was a theory that co-ordinated many hitherto iso- 
lated observations and that stimulated scientific enquiry. Under its 
aegis a remarkable band of eighteenth-century investigators accumu- 
lated the evidence and worked out the experimental technique that 
led to its fall, late in the century. Chief among them were Black (Scot- 
land), Priestley and Cavendish (England), and Scheele (Sweden). 

Black (1728-1799) was professor of chemistry at Edinburgh from 
1766 to 1799, during "the golden age of Edinburgh society." A precise 
and confirmed bachelor, "he sung, and performed on the flute, with 
great taste and feeling; and could sing a plain air at sight" which is 
more than can be said of many (if any) professors of chemistry in the 
present age of intense specialization. Black (1755) showed that heated 
chalk or marble gave much less than its weight of quicklime, the loss 
being due to the expulsion of "fixed air" (carbon dioxide), a gas 
which Black collected and characterized. Black's discovery that fixed 
air could be differentiated from common air, that it could be held in 
solid combination in chalk or marble, and that it could be weighed in 
that state, contained the germ of Lavoisier's later theory of combus- 
tion. Besides this, Black's use of the balance in following chemical 



164 What Is Science? 

changes inaugurated another profound advance, this time in the de- 
velopment of quantitative chemistry. Modern chemistry owes its birth 
to the use of the balance and other instruments of precision in follow- 
ing chemical changes quantitatively. The qualitative observation that 
chalk decomposes into quicklime and carbon dioxide is only the first 
of two steps necessary in studying this chemical change; the next step 
a vital one is to ascertain by experimental measurement what 
weight of lime and what volume (and eventually weight) of carbon 
dioxide are yielded by a known weight of chalk. This is the quantita- 
tive step. 

Priestley (1733-1804), the son of a humble Yorkshire cloth dresser, 
became a brilliant amateur of science, whose discoveries, sometimes 
made at random, were of profound significance. His unorthodox and 
advanced views, especially in politics, made him the victim of mob 
violence, and he emigrated to America, ending his days at Northum- 
berland, Pennsylvania. Priestley devised methods of isolating and han- 
dling gases effectively. He introduced the pneumatic trough, and col- 
lected his gases not only over water, as Boyle, Mayow and Hales had 
already done, but also over mercury, thereby discovering sulphur di- 
oxide, ammonia, hydrogen chloride, and other gases which dissolve in 
water. The pneumatic trough consists of a vessel in which an inverted 
jar filled with a liquid (usually water) is supported on a perforated 
shelf submerged in the same liquid; a gas rising from a tube dipping 
beneath the jar is thus collected in it. 

Priestley seems to have regarded his various gases, or "airs/' as com- 
mon air associated with different amounts of phlogiston. In 1774 he 
made a discovery, at Calne in Wiltshire, that was destined to exert a 
trigger-like action on the development of chemistry. August 1 in that 
year is a date rarely to be found in history books, yet it is one of 
tremendous significance in the record of human progress; for it was on 
this day that Priestley discovered oxygen, by heating some red calx of 
mercury (mercuric oxide) with a new burning glass of a foot in 
diameter, the calx being put into a glass tube closed at the upper 
end, "filled with quicksilver, and kept inverted in a bason of the 
same." 

This gas supported combustion with unprecedented vigor. "A piece 
of red-hot wood sparkled in it, exactly like paper dipped in a solution 



Chemistry 165 

of nitre/' wrote Priestley; and a mouse "remained perfectly at its ease" 
in the gas for twice the time it would have lived in an equal amount 
of common air, and was alive and kicking when taken out. Priestley 
therefore concluded that this gas was air completely deprived of phlo- 
giston, and so named it "dephlogisticated air." 

Oxygen was discovered independently by Scheele (1742-1786), a 
great pioneer of qualitative chemistry, who in his short span of life 
discovered oxygen, chlorine, tungstic acid, numerous organic acids, 
glycerol, and many other substances. This struggling pharmacist, 
whose memory is honored in Stockholm by a handsome statue, once 
wrote to a friend: "You may think perhaps that material cares are go- 
ing to absorb me, and take me away from experimental chemistry. 
Not so! That noble science is my ideal." 

From the struggling Swedish apothecary the chemical scene changes 
to disclose Cavendish (1731-1810), the eccentric and aloof million- 
aire, grandson of an English duke, with "a peevish impatience of the 
inconveniences of eminence," a dislike of women, of all meats save 
mutton, and of all towns save London. As a scientist, this enigmatic 
figure was richly endowed with the quantitative instinct and with su- 
perb manipulative skill. He characterized various gases ("factitious 
airs") by measuring their specific gravities. lie analyzed common air, 
showing that it contained just over 20 per cent of "dephlogisticated 
air" (oxygen); also he found that when a mixture of two volumes of 
"inflammable air" (hydrogen) with one volume of "dephlogisticated 
air" was exploded, the sole product was water, the two gases disap- 
pearing in the process. These researches led quickly to the elucidation 
of the chemical nature of the ancient "elements," air and water. 

Now, as so often in the history of science, a point had been reached 
at which the known facts enabled a tremendous step forward to be 
taken. The only remaining obstacle was a mental one; for one of the 
most difficult of all mental processes is to reassemble a series of fa- 
miliar facts and relationships and to regard them from a new view- 
point. 

In this ability lay the great genius of Lavoisier, who, without mak- 
ing a single discovery of any new body, or property, or natural phe- 
nomenon, demolished in the 1780s the barrier that had hitherto 
blocked progress in chemistry. By carefully planned quantitative ex- 



166 What Is Science? 

periments he showed that the air absorbed by heating mercury in 
a closed vessel was equal in volume to the "dephlogisticated air" pro- 
duced by heating more strongly the resulting red calx of mercury. This 
simple and logical experiment sealed the fate of the phlogiston the- 
ory: it showed that the calx was a compound of mercury with "de- 
phlogisticated air/' the active atmospheric constituent which Lavoisier 
now called oxygen. So arose the modern "theory of combustion/' 
Passing to the problem of the constitution of water, Lavoisier first 
confirmed Cavendish's synthetical experiments, and then devised the 
analytical method of passing steam over heated iron filings contained 
in a gun barrel, thereby verifying his prediction that when oxygen 
was abstracted from water by the iron, to form a substance akin to 
ordinary rust, free hydrogen would remain. 

Lavoisier (1743-1794) was a lawyer, a scientist, and a prominent 
figure in the public life of France. His execution in 1794 was perhaps 
the most insensate of all the crimes of the French Revolution. "La 
Republique n'a pas besoin de savants/' pronounced the egregious 
Coffinhal, president of the tribunal; but Lagrange gave expression to 
the sobered feelings of France in the words: "II ne leur a fallu qu'un 
moment pour faire tomber cette tete, et cent annees peut-etre ne 
suffiront pas pour en reproduire une semblable." In conformity 
with this thought, Pasteur, who ranks beside Lavoisier as one of the 
three or four greatest men that France has produced, died almost ex- 
actly a century later (1895). 

The abolition of the old theories and the accumulation of accurate 
quantitative data led rapidly to the formulation of that comprehen- 
sive "Atomic Theory" whose innumerable ramifications form the nerv- 
ous sytem of the wonderful body of physical science as we know it 
today. Dalton (1766-1844) began his career as a humble Quaker 
schoolmaster in a Cumberland village. Unlike Cavendish, although 
he remained a bachelor, Dalton, "like most men of higher sensibility 
and intelligence, greatly enjoyed the society of ladies, provided that 
they were women of superior talents and mental culture." The first 
printed account of Dalton's theory appeared in 1807. Epicurus, as 
long ago as 300 B.C., held that matter was discontinuous or grained; 
and this conception may be traced back through Democritus to Leu- 
cippus, in the sixth century B.C. Dalton's conception of an atomic 



Chemistry 167 

constitution of matter was derived from Newton rather than from the 
ancient Greeks. He converted a vague speculation into a precise the- 
ory: this was based upon laws resting in turn upon quantitative ex- 
perimental data. 

Newton had pictured the atom as a "hard, impenetrable, movable 
particle ... so very hard as never to wear or break in pieces: no or- 
dinary power being able to divide what God himself made One, in 
the first creation." The idea that matter is uncreatable and indestruc- 
tible led to the so-called law of the conservation of matter, a con- 
ception inherent in Dalton's atomic theory. Dalton held that the 
multitudinous substances of the material world are built up from a 
limited number of kinds of atoms, corresponding to the different ele- 
ments, all the atoms of a particular clement being alike and having 
the same weight. He regarded the formation of compounds as de- 
pendent upon combination between small whole numbers of atoms 
of the elements concerned, the resulting "compound atoms" (now 
known as molecules] of a compound being again alike and having the 
same weight. 

These conceptions, or postulates, led to the establishment, by ex- 
perimental observations, of three main laws which formed the orig- 
inal foundations of Dalton's atomic theory. (1) The law of fixed pro- 
portions (or constant composition) states that the elements combine 
together in fixed proportions by weight; in other words, the same 
chemical compound always consists of the same elements combined 
together in the same proportions. For example, pure water, however 
obtained or prepared, always contains one-ninth of hydrogen and 
eight-ninths of oxygen by weight. 

(2) The law of multiple proportions states that when two ele- 
ments unite to form more than one compound, the different weights 
of one which combine with a constant weight of the other bear a 
simple ratio to each other. Thus, hydrogen and oxygen give rise to 
(a] water, and (b) hydrogen peroxide, containing 11.11% and 
5.88% of hydrogen, respectively. The weights of oxygen combining 
with one part by weight of hydrogen are therefore 8 parts in water and 
16 in hydrogen peroxide, these being in the simple ratio 1:2. 

(3) The law of reciprocal proportions states that the proportions in 
which two elements combine separately with a third element are in a 



168 What Is Science? 

simple ratio to those in any compound of the first two elements. For 
example, 1 part by weight of oxygen combines with 0.125 part of 
hydrogen (to form water), or with 0.875 part of nitrogen (to form 
nitric oxide). The proportions here are 0.125 (hydrogen) to 0.875 
(nitrogen), or 1:7. The first two elements, hydrogen and nitro- 
gen, combine together (to form ammonia) in the proportions 1 
to 4.67, or 1 1/2:7. The "simple ratio" is thus 1/7 to P/2/7, or 2:3. 

A little thought will show that the conclusions summarized in these 
three laws are logical consequences of Dalton's original postulates. 

Although excessively minute, each kind of atom has its distinctive 
atomic weight. The absolute weight (or mass) of the hydrogen atom 
is now known to be 1.66 x 10~ 24 gram; but since originally the ab- 
solute weights could not be determined, the atomic weight of the 
lightest element, hydrogen, was taken as unity, and the relative weights 
of other kinds of atoms were based upon this standard. In the early 
days of the atomic theory the determination of these relative atomic 
weights, by accurate analytical methods, owed much to the practical 
skill of the eminent Swedish chemist, Berzelius (1779-1848). 

Dalton, following the alchemical tradition, used symbols to repre- 
sent simple atoms and "compound atoms" (molecules); but Berzelius 
replaced these symbols by letters. The first six Daltonian symbols re- 
produced below (Fig. 4) represent, in order, the elements hydrogen, 
nitrogen, carbon, oxygen, phosphorus, and sulphur. The second line 
shows the "arbitrary marks or signs" for a "compound atom" (mole- 
cule) of each of the following compounds: water, ammonia, nitrous 
gas (nitric oxide), olefiant gas (ethylene), and carbonic oxide (car- 
bon monoxide). 



o e o 

.GO GO (DO O0 O 

Fig. 4 Some Daltonian symbols. 

In modern chemical notation the literary symbol stands for one 
atom of the element it represents, so that the equivalents of the above 
symbols would be H, N, C, O, P, S, for the elements; and IIO, UN, 
NO, HC, OC for the compounds. Each of these last five would now 



Chemistry 1 69 

be called a molecular formula, which is an expression of the kind 
and number of each atom in the molecule concerned. The correct 
molecular formulae for the five compounds shown above arc, in fact, 
II 2 O, NH 3 , NO, C 2 II 4 , and CO. Often it is inconvenient to use the 
first letter of the name as the symbol of an elementary atom, some 
common examples being: Cu, copper; Au, gold; Fe, iron; Pb, lead; 
Hg, mercury; K, potassium; Ag, silver; Sn, tin. 

With the discovery and examination of more and more elements it 
became possible for Newlands (1838-1898), a chemist in a London 
sugar refinery, to expound a so-called law of octaves in papers pub- 
lished between 1863 and 1866. lie pointed out that when the ele- 
ments were arranged in the order of increasing atomic weights, each 
element showed a family likeness to elements which were seven, or 
some multiple of seven, places before or after it. lie was however dis- 
couraged by the cold reception of his idea, especially when a member 
of an audience of the Chemical Society of London asked him whether 
he had ever thought of looking into an alphabetical arrangement! 

Other chemists pursued the idea of a systematic classification, and 
in 1869 the Russian chemist Mcndelecff (1834-1907), the youngest 
of a family of fourteen children, who became professor of chemistry 
in St. Petersburg, published a comprehensive arrangement known as 
the "periodic system/' in which he showed that the elements, when 
arranged in the order of increasing atomic weights, fell into definite 
families or groups, showing a periodicity of chemical and physical 
properties. Without going into details, the following sequence (Fig. 
5) may be taken from the current periodic table in illustration, the 
symbol and atomic weight of each element being given below its 
name: 

HELIUM LITHIUM BERYLLIUM BORON CARBON NITROGEN OXYGEN FLUORINE 

Me 4 Li 7 Be 9 B 11 C 12 N 14 O 16 F 19 

ALUMI- PHOS- 

NEON SODIUM MAGNESIUM NUM SILICON PHORUS SULPHUR CHLORINE 

Nc 20 Na 23 Mg 24 Al 27 Si 28 P 31 S 32 Cl 35.5 

GROUP 

O I II III IV V VI VII 

Fig. 5 Part of the Periodic Table of Elements. 



170 What Is Science? 

Group O contains the rare gases of the atmosphere, helium, neon, 
argon, etc., which are distinguished from all other elements by their 
abnormal chemical stability and unreactivity. Group I is the family 
of the alkali metals, lithium, sodium, potassium, etc. These soft, sil- 
very metals decompose water readily, liberating hydrogen; simul- 
taneously they form strongly alkaline solutions of sodium hydroxide 
(caustic soda), etc. Group VII, known as halogens, combine with 
hydrogen giving rise to acids, such as hydrochloric and hydrobromic 
acids; these acids, in turn, react with the alkaline hydroxides of 
Group I to form salts: hydrochloric acid and sodium hydroxide, for 
example, react to yield sodium chloride (common salt, NaCl) and 
water. 

Mendeleeff ascribed certain gaps in his classification to the exist- 
ence of undiscovered elements, and soon afterward some of these 
were discovered and found to have the very properties predicted by 
Mendeleeff. Such relationships, when well established, gave rise to 
much speculation concerning their fundamental cause, and attention 
became increasingly focused upon the nature of the atom. Were the 
elements possibly the result of variations upon an atomic theme, 
dependent ultimately upon atomic structure? If so, Dalton's concep- 
tion of an unbreakable particle, not possessed of any organized struc- 
ture, would have to be abandoned, carrying with it a celebrated 
aphorism of the great Quaker man of science: "Thou knows no man 
can split an atom/' 

Meanwhile, from about 1850 onward, physicists had devoted 
growing attention to the study of electric discharges in high vacu- 
ums. With the refinement of experimental technique in physical sci- 
ence, which became increasingly apparent toward the end of the 
nineteenth century, researches in this field culminated, in 1897, in 
the discovery by J. }. Thomson (1856-1940), Cavendish professor of 
experimental physics at Cambridge, of a particle of matter having 
only l/1840th the mass of a hydrogen atom. This lightest of all 
particles, obtained from various kinds of matter, was identified as a 
unit of negative electricity and given the name of electron. Thus 
arose the conception of the "electronic constitution of the atom" and 
consequently of matter. After much further experimental work of a 
physical nature, the atom gradually took shape according to the views 



Chemistry 171 

of Rutherford (1871-1937), who succeeded his old master, J. J. Thom- 
son, at Cambridge, Bohr (b. 1885), professor of physics at Copen- 
hagen, and others, as a positively charged nucleus surrounded by re- 
volving electrons in different numbers characteristic of the particular 
kind of atom. The nucleus, which accounts for practically the whole 
mass of the atom, is pictured as an aggregate of positive and negative 
electrical units, known as piotons and electrons, these being present 
in the form of protons and neutrons (proton-electron pairs). The 
number of protons (apart from those of the neutrons) in the nucleus 
is identical with the atomic number, or serial number of the element 
in the revised periodic classification. 

Some typical atomic structures are shown diagrammatically in Fig. 
6: the nucleus is indicated as a circle enclosing protons (p) and neu- 
trons (n), and the extranuclear electrons (e) are shown outside the 
circle; the atomic weight (A.W.) and atomic number (A. No.) are 
also noted. 




Hydrogen, 
A. W. 1 
A. No. 1 






Neon, 
A. W. 20 

A, No. 10 

Fig. 6 Diagrammatic structures of atoms. 



Sodium, 
A.W. 2? 
A. No. 11 



Protons ( + ) and electrons ( ) have equal and opposite elec- 
trical charges. In a normal atom the positive nuclear charge is neu- 
tralized by extranuclear, or planetary, electrons, the total number of 
electrons and protons in the atom being equal. The gain or loss of a 
planetary electron destroys the electrical balance of negative and posi- 
tive charges, and gives rise to a charged atom, or ion. The planetary 
electrons revolving in closed orbits about the nucleus are depicted in 
shells (layers or levels), these forming stable assemblages when they 
contain 2 (in the innermost shell), 8, 18, or 32 units. The neutral 
atom of sodium and the derived sodium ion (carrying 1 positive 
charge) are represented in Fig. 7. 

The chemical character of the atom depends upon the number of 
electrons in its outermost shell: these, the so-called valency electrons, 



172 What Is Science? 





Sodium Atom Sodium Ion 

Fig. 7 Diagram of a sodium atom (electrically neutral) and a sodium 

ion ( electropositive ) . 

do not usually exceed eight. Newlands' law of octaves (1863) is thus 
seen to be an expression of the recurrence of chemical properties due 
to the building up of the valency electrons from one to eight. Each 
member of a natural family of elements has the same number of 
valency electrons. 

A modern form of classification of the elements is shown in Fig. 8, 
which gives the atomic numbers of the elements and also summarizes 
their arrangement into Groups I-VII and O. (The so-called rare- 
earth elements (58-72) are not shown individually.) Altogether 
ninety-two elements have been discovered in nature, ranging from hy- 
drogen (H, atomic number 1, atomic weight 1) to uranium (U, 
atomic number 92, atomic weight 238). In addition a few other 
purely artificial elements (93 onward) have been produced. 

As stated above, the chemical nature of an atom depends upon the 
extranuclear electrons. The same number and arrangement of these 
may be associated with more than one kind of nucleus. This possibil- 



-87 Fr 

-88 Ra 
80. Ac- 



Croup 
I 1. 
II 
HI 
IV 
V 
VI 
VII 



3. Li - 11 Na 

4 Be 12 Mg 

5 B - 13 Al 

6 C - H Si 

7 N - IS. P 

16 S 

17 Cl 



3 Q 
\ F 



0. 2. He 10. Ne 18 A 



37 Rb- 

33 St- 

39 Yt- 

40 Zr 

41 Nb 

42 Mo 

43 Tc 

44 Ru 
15 Rh 
46 IM 
47. Ag- 

48 Cd 

49 In- 

50 Sn - 

5 1 Sb- 
52 




90 Tli 

91. Pa 

92. U 

93. Np 

94 Pu 

95 Am 

96 Cm 

97 Bk 

98 Cf 
99. 



Fig. 8 A modern table of the elements. 



Chemistry 173 

ity accounts for the formation of isotopes, which are atoms with sim- 
ilar chemical properties and the same atomic number but different 
atomic weights. Most elements can exist in isotopic forms. For ex- 
ample, there are three known isotopic forms of hydrogen and three 
of uranium (Fig. 9). Ordinary hydrogen consists of about 6000 parts 
of protium mixed with 1 part of deuterium; tritium is a purely arti- 
ficial isotope. A very small proportion of deuterium oxide ("heavy 
water"), D 2 O, exists in natural waters. 



Protium, 
'H 




Deuterium, 
2 H or D 




Uranium 238 




Uranium 235 

23.-.TJ 




Uranium 234 

234 IJ 



Fig. 9 Isotopic forms of hydrogen and uranium (diagrammatic). 

The modern theory of the ultimate constitution of the chemical 
elements takes us back to Aristotle's idea of a primordial matter and 
the derived alchemical tenet of the unity of matter. Plato, some 
twenty-three centuries ago, held the view that nature is based upon a 
mathematical plan, and that the ultimate realities must be sought in 
mathematics. How right he was! Going still farther back in time, 
the electronic theory of the constitution of matter may be regarded 
as the latest expression of the primitive doctrine of the two contraries: 
the human mind, like the electrons it has bodied forth, seems to 
work in closed orbits. 

In all ordinary chemical processes atoms are quite stable and be- 
have as if they were indivisible particles. However, evidence was forth- 
coming from 1896 onward that some of the elements of very high 
atomic weight, such as uranium (238) and radium (226), exhib- 
ited the phenomenon of radioactivity, which was later traced to 
spontaneous atomic disintegration into atoms of a different kind, 
energy being continuously emitted in the process. This was tanta- 
mount to natural transmutation, and in 1919 Rutherford brought 
about the first artificial transmutation by "bombarding" nitrogen 



174 What Is Science? 

atoms with the so-called a-particles (helium nuclei), which are pro- 
jectiles of tremendous kinetic energy emitted by radium atoms. Ni- 
trogen was thus transmuted into oxygen; and similarly beryllium gave 
rise to carbon. These atomic nuclear changes were accomplished only 
on a tiny scale, but it was noticed that the amount of energy liberated 
was enormous in comparison with that of the most energetic chemi- 
cal reaction (in which the atoms remain unchanged). In all such ex- 
amples investigated before 1938, however, the total energy supplied 
by the bombarding particles was much greater than the liberated en- 
ergy, and the process required continuous bombardment. 

By means of a laborious process, uranium 235 (Fig. 9) may be 
separated from natural uranium, of which it constitutes only about 
0.7%. In 1938 it was discovered that upon bombarding this uranium 
isotope with neutrons, a self-propagating process was set up, due to 
the continuous release of fresh neutrons in an atomic fission or 
nuclear disintegration accompanied by a release of energy incompara- 
bly greater than that furnished by the most powerful organic explo- 
sive. It was a deplorable tragedy for humanity that the first applica- 
tion of this new and marvelous source of energy should have taken 
the shape of an "atomic bomb." One of the greatest problems now 
facing science is to achieve control of atomic power or nuclear 
energy, enabling it to be applied as a convenient source of heat, light, 
and locomotion. Perhaps the greatest of all human problems is to 
prevent the misuse of atomic energy: "We must indeed pray," said 
Mr. Winston Churchill in 1945, "that these awful agencies will be 
made to conduce to peace among the nations, and that instead of 
wreaking measureless havoc upon the entire globe they may become 
a perennial fountain of world prosperity." 

Returning now to ordinary chemistry, atoms usually form combina- 
tions called molecules, instead of remaining in a state of "single 
blessedness," for reasons explained below. The molecule of ordinary 
hydrogen is formed by the mutual linkage of two atoms, and is 
written H 2 . The water molecule, H 2 O, contains two atoms of hydrogen 
and one of oxygen; similarly the molecule of ammonia is written 
NH 3 and that of methane CH 4 . The molecules of a particular sub- 
stance are all alike. The molecules of elements contain only one 
kind of atom; those of compounds contain two or more kinds of 



Chemistry l/0 

atoms. Any change which leaves the molecules intact, such as con- 
version from solid into liquid, or liquid into gas, is a physical change; 
any change which breaks them open, such as the decomposition of 
water into hydrogen and oxygen, is a chemical change. 

A very important general property of molecules was first stated 
in "Avogadro's hypothesis" (1811), according to which equal vol- 
umes of all gases, under the same conditions of temperature and pres- 
sure, contain the same number of molecules. In gases we perceive a 
picture of the final condition of a completely democratic society: 
their constituent units (molecules) have the same "living space"; 
they display no individuality or originality, and are precisely alike in 
every respect. 

The molecular formula of a substance, such as H 2 , H 2 O and NH 3 , 
given above, shows the name and number of each kind of atom in 
the molecule; it is obtained by a simple numerical calculation from 
a knowledge of the relative atomic weights of the constituent ele- 
ments and the percentage composition (found by chemical analysis) 
and molecular weight of the substance. The molecular weight is the 
weight of the molecule referred to the weight of a hydrogen atom 
as unity; it is most readily obtained by comparing the vapor density 
of the substance with the density of hydrogen gas, applying Avoga- 
dro's hypothesis, and taking into account the fact that the hydrogen 
molecule contains two atoms. 

According to the "Theory of Valency," first advanced in 1852 by 
Frankland (1825-1899), professor of chemistry at Manchester, 
each kind of atom has a definite combining capacity or valency (va- 
lence), expressible as a low whole number. The univalent hydrogen 
atom is written H ; the bivalent oxygen atom, O . The strokes 
represent so-called valency bonds or points of attachment of one atom 
to another. The water molecule may thus be shown as H O H in 
a structural formula, showing how the atoms are linked together in 
the molecule. An atom often varies in its valency; for example, the 

H 

nitrogen atom is 3-valent in ammonia, H N H, and 5-valent in 
nitric acid (HNO 8 ), H O N^ . This last structural formula 



176 What Is Science? 

shows both single bonds and double bonds between atoms; triple 
bonds are also known. 

The later "electronic theory of valency" depicts the nature of these 
bonds, of which there are two main types. As a simple example of 
covalency, the molecule of hydrogen is held together through 
each atom sharing its single valency electron with the other, 
H. -f-'H-*H : H, thus forming a stable (innermost) shell of two 
extrariuclear electrons for each hydrogen atom. Or again, the covalent 
compound, methane or marsh gas, CH 4 , may be formulated electron- 
ically as shown in Fig. 10, in which the four valency electrons of the 
carbon atom are represented by small open circles: the carbon atom 
shares its four electrons with those of four hydrogen atoms, thereby 
enabling each hydrogen atom to achieve its stable shell of two elec- 
trons and the carbon atom to complete its stable shell of eight elec- 
trons, a so-called octet. Single bonds are here concerned. A double 
bond is formed through the sharing of four electrons, of which each 
atom contributes two, as in the molecule of carbon dioxide, CO:*, in 
which each constituent atom has completed its stable octet: 



'<> 



H 
H-C-H 


H 

HCSH 


^ 


H 


(I) 


(") 



(I) (H) 

Fig. JO Ordinary structural formulae (I) and electronic formulae (II) 
for methane and carbon dioxide. 

The covalency, or nonpolar bond, represents one main type of 
interatomic combination. Another type, of equal importance, is the 
electrovalency, or polar bond. For example, in sodium chloride (com- 
mon salt), NaCl, the sodium atom transfers its sole valency electron 
to the chlorine atom which already has seven valency electrons: thus 
a stable octet of eight valency electrons is built up as the outermost 
shell of each of the two atoms. The sodium atom is now positively 
charged (through losing an electron) and the chlorine atom is nega- 
tively charged (through acquiring one): the two atoms arc held to- 
gether by electrostatic attraction, or linked by a polar bond. Such 



Chemistry 177 

substances, unlike those of the first type, tend to sever into oppositely 
charged ions, especially in solution. In the following representation, 
which should be compared with Fig. 7, only the outermost shells of 
valency electrons (each shown by a dot) are denoted: 

Na- + .Cl: -> Na Cl: -^ [Na]+ [:C1:]-. 

All salts of acids and bases are particularly prone to ionization owing 
to the occurrence of polar bonds; but covalcnt compounds, including 
notably the great majority of organic compounds, do not show this 
tendency. According to the theory of electrolytic dissociation, acids 
and bases arc ionic compounds, yielding, respectively, hydrogen ions 
[II] + and hydroxyl ions [O1I]~ in aqueous solution. 

The modern chemist has to think simultaneously in two ways, the 
qualitative and the quantitative; these two kinds of relationships, 
which attend all chemical change, are conveniently embodied in a 
concise notation, finding one of its most useful forms in the chemical 
equation. For example, the reaction between nitric acid and sodium 
hydroxide, giving rise to sodium nitrate and water, may be sum- 
marized in the equation: IINO 3 + NaOH = NaNO 3 + H 2 O. Writ- 
ten in the ionic way this becomes: 

[H]+ + [N0 3 ]- + [Na]+ + [Oil]- = [Na] + + [NO 3 ]- + H 2 O 

(water being almost non-ionized). In general, an acid reacts with a 
base to form a salt and water. 

To pursue further the information summarized in a chemical equa- 
tion, we may take the simple example: ZIL + O L > = 2H 2 O. This 
shows that 4 parts by weight of hydrogen (atomic weight, 1 ) combine 
with 32 parts by weight of oxygen (atomic weight, 16), to form 36 
parts by weight of water; also (by Avogadro's hypothesis) that, at the 
same temperature and pressure, 2 volumes of hydrogen and 1 of oxy- 
gen yield 2 volumes of gaseous water (steam). 

A still more complete equation shows the energy-change concerned, 
and gives the exact amount of heat produced in this exothermic re- 
action, 2IL + O 2 2ILO (liquid) + 136.8 calories. The equation 
means that the combination of 4 grams of hydrogen and 32 grams of 
oxygen gives rise to 36 grams of water, in the liquid form, with the 



178 What Is Science? 

evolution of 136.8 calories of heat. Conversely, the decomposition 
of 36 grams of liquid water into hydrogen and oxygen requires ex- 
actly the same quantity of heat or other form of energy. Nature is 
a strict accountant in all such processes. In certain other chemical 
changes, called endothermic, heat is absorbed. Here we encounter 
an elementary aspect of "thermochemistry," which in turn forms part 
of a major branch of the science known as PHYSICAL CHEMISTRY, 
concerned with the study of physical properties in relation to chemical 
constitution and chemical change. Physical chemistry, like physics, 
has become increasingly mathematical in its development. 

The elements combine together in a practically unlimited number 
of ways, determined by their valencies and chemical nature, to form 
molecules of many grades of complexity, ranging from hydrogen 
molecules, H 2 , with two like atoms, to molecules built up of various 
kinds and numbers of atoms. It was realized in due course that of all 
these distinct forms of matter (substances, or chemical compounds) 
which gradually became known, some occurred in lifeless mineral 
matter, while others were invariably found in association with living, 
or "organized" matter. A distinction was thus recognized in the 
eighteenth century, between inorganic and organic substances. 
Thus arose the two great divisions of this science known as INORGANIC 
CHEMISTRY and ORGANIC CHEMISTRY. 

Among the great variety of inorganic materials are, for example, 
the gases of the atmosphere, water, rocks, minerals, metals and their 
oxides and salts, nonmetals and their compounds, such as sulphuric 
and hydrochloric acids, and so forth. Natural organic materials in- 
clude plant and animal fats, carbohydrates, proteins, dyestuffs, alka- 
loids, perfumes, alcohol, organic acids, rubber, coal, petroleum, and 
so on, in almost endless variety. A glance at such lists is sufficient to 
indicate that all the great manufacturing industries, including agri- 
culture, the oldest industry of all, depend upon these two great 
branches of chemistry; it is evident also that the raw materials of the 
world can be applied economically to industrial purposes only by the 
application of systematic chemical methods. Inorganic chemistry is 
linked closely to geology, mineralogy, and metallurgy; organic chem- 
istry to physiology, biochemistry, and biology in general. 
Early in the nineteenth century it was realized that all the so- 



Chemistry 179 

called natural organic compounds contain carbon as a constituent 
element. At the present day many of the natural organic compounds 
have been synthesized by artificial processes; moreover, thousands of 
artificial carbon compounds unknown in nature have been produced. 
Organic chemistry embraces all these compounds; so that now organic 
chemistry is the chemistry of the carbon compounds. Inorganic chem- 
istry embraces all the others. 

Carbon compounds outnumber those of all other elements added 
together, although they are composed chiefly of carbon in combina- 
tion with hydrogen, oxygen, and nitrogen: C, II, O and N are the 
"Big Four" of organic chemistry. The cause of this prodigality first 
came to light when Kekule (1829-1896), professor of chemistry at 
Ghent and later at Bonn, whose ideas were born in a series of vi- 
sions, published his "theory of organic molecular structure" in 1858. 
This theory is based upon two simple postulates: (1) the 4-valency 
of carbon atoms, and (2) the capacity of carbon atoms to link to- 
gether. Kekule relates that he fell into a reverie upon a London om- 
nibus, late at night, "and lo, the atoms were gamboling before my 
eyes! ... I saw how, frequently, two smaller atoms united to form 
a pair; how a larger one embraced two smaller ones; how still larger 
ones kept hold of three or even four of the smaller; whilst the whole 
kept whirling in a giddy dance. I saw how the larger ones formed a 
chain, dragging the smaller ones after them . . . This was the origin 
of the Theory of Molecular Structure." 

In the simplest organic types, known as hydrocarbons, the spare 
valencies of the carbon atoms forming these chains are taken up 
solely by hydrogen atoms. In a simple chain, such as C C C C, 
each of the end (primary) carbon atoms needs three hydrogen atoms, 
and each of the intermediate (secondary) ones needs two, to take up 
the unsatisfied valencies of the 4-valent carbon atoms. In this specific 
example the structural formula of the hydrocarbon will thus be 
CH 3 CH 2 CH 2 CH 3 . Lengthening the carbon chain will be 
tantamount to introducing more bivalent CH 2 groups. It fol- 
lows that organic compounds may be arranged in so-called homolo- 
gous series, adjacent members of which have the common molecular 
difference CH 2 . 

Hydrocarbons occur plentifully in nature, particularly in natural 



180 What Is Science? 

petroleums, which consist almost entirely of such substances. Penn- 
sylvanian petroleum is rich in a homologous series known as the 
paraffin series, the first four members of which are methane, CH4 
(compare Fig. 10); ethane, C 2 H 6 (molecular formula), or CII 3 
CH 3 (structural formula); propane, C 3 H 8 , or CH 3 CH 2 CH 3 ; 
and butane, C 4 Hio, or CH 3 CH 2 CH 2 CII 3 , which may be 
written more compactly as CII 3 (CH 2 )2 CH 3 . This homologous 
series, having the general molecular formula C n H 2rH _ 2 , in its natural 
occurrence may have up to about 70 carbon atoms in the molecule. 
Its simple members are gases (as in "bottled gas"); then come liquids 
(as in gasoline, lubricating oils, etc.), followed by solids (as in paraffin 
wax). 

From butane onward in this series the molecular formula is no 
longer unequivocal, since it may be expanded structurally in more 
than one way. For example, there are two butanes, C 4 Hi , namely, 
CH 3 (CH 2 ) 2 ~ CH 3 (normal or n-butane), and CH 3 CH CH 3 

! 

CH 3 

(zsobutane). The first molecule contains an unbranched, and the 
second a branched, chain of 4 carbon atoms. This is a simple example 
of structural isomerism. The two compounds are called isomers y that 
is, substances which are distinctive, although having the same molecu- 
lar formula, because the atoms are differently arranged within their 
molecules. Isomerism is very rare in inorganic chemistry, but it per- 
meates organic chemistry in many forms. With the more complex 
formulae the number of possible isomers approaches astronomical 
dimensions; for instance, the relatively simple molecular formula, 
C3 H 62 , in the paraffin scries (containing only two kinds of atoms), 
corresponds theoretically to more than 4,000 million isomers rendered 
possible solely by the great diversity of ramified carbon chains. 

No other element except carbon shows more than a rudimentary 
capacity for the self-linking of its atoms. It is this unparalleled prop- 
erty of the carbon atom, taken in conjunction with its 4-valency, 
that accounts for the practically unlimited number of carbon com- 
pounds, and hence for the existence of the vast realm of organic 
chemistry. 

Sometimes two adjacent carbon atoms arc linked bv a double bond 



Chemistry 181 

of two covalencies, like the carbon and oxygen atoms in the molecule 
of carbon dioxide (Fig. 10). The simplest example is seen in the 
hydrocarbon ethylene (or cthene), C 2 II 4 , which is shown structurally 
as H 2 C = CII 2 . Triple bonds arc possible also, the simplest example 
being acetylene (or ethyne), C 2 H 2 , with the structural formula, 
IIC^CII. Double and triple bonds arc vulnerable or reactive po- 
sitions in the molecules of such substances, which are called unsatu- 
rated, in contradistinction to saturated substances, like the paraffin 
hydrocarbons, which have no double or triple bonds in the molecule. 
The reactivity of ethylene is shown, for example, by its ability to 
acquire two extra atoms of hydrogen per molecule, when mixed with 
hydrogen gas in presence of a suitable catalyst (such as finely divided 
nickel): thereby it undergoes catalytic hydrogenation, passing into 
the saturated hydrocarbon, ethane: C 2 H 4 -f- 211 = Colic- This is a 
typical example of an addition reaction, characteristic of unsaturated 
substances. 

A catalyst is a substance of which a comparatively small amount 
can promote a chemical reaction without itself undergoing any per- 
manent change or loss. It probably acts either through the formation 
of unstable intermediate compounds, or through the production on 
its surface of a high concentration of the reacting substances. 

Theoretically, hydrocarbons may be regarded as the parent com- 
pounds of a great variety of other organic types, in which various 
hydrogen atoms are replaced by other atoms or groups of atoms. It 
docs not follow that this pictured replacement, or substitution, may 
be experimentally feasible; even if it is, the process may not provide 
the best way of preparing the substitution product. For example, 
ordinary alcohol (ethyl alcohol) may be regarded as hydroxy-ethane, 
C 2 II 5 OH, in which one of the six hydrogen atoms of ethane has 
been replaced by the univalent hydroxyl group, OH. Actually, 
ethyl alcohol can be prepared from ethane in two stages, summarized 
in the following equations: (1) C 2 H fl + C1 2 = HC1 + C 2 H B Cl 
(ethyl chloride); (2) C 2 H 5 - Cl + NaOH = NaCl + C 2 H 5 - OH. 
Each of these equations represents a substitution reaction, character- 
istic of saturated substances. In practice however alcohol is prepared 
by fermenting sugars, such as glucose, C 6 Hi 2 O 6 , this reaction being 
induced by a complex organic catalyst, or enzyme, called zymase, 



182 What Is Science? 

which is produced in certain living microorganisms known as yeasts: 
C 6 H 12 O 6 = 2C 2 H 6 O + 2CO 2 . 

The typical group of all alcohols is OH, attached directly to a 
saturated carbon atom. This group is not ionized, like the OH 
group of sodium hydroxide, since it is attached to the carbon atom 
by a covalent bond. Indeed, the covalency is almost invariable in or- 
ganic chemistry, except in specific parts of the molecules of organic 
acids, bases, and salts, which like their inorganic analogues, are ioniz- 
able. With such exceptions, organic compounds do not undergo 
ionization. Of the great variety of other typical groups of organic 

^ 
chemistry, the carboxyl group C\ , of organic acids, and the 

X OH 

^O 
aldehyde group, Cf , may be mentioned. Simple examples are 

found in acetic acid, CH 3 COOH, and acetaldehyde, CH 3 CHO. 

These, and many other organic compounds, may now be synthe- 
sized, or built up in a series of chemical processes, from elementary 
carbon, in such forms as coke or charcoal. At a very high temperature, 
usually produced by hydroelectric energy in the electric furnace, car- 
bon reacts with lime (calcium oxide, CaO) to form calcium carbide 
and carbon monoxide: CaO + 3C = CaC 2 + CO. Water acts on 
calcium carbide to give acetylene and calcium hydroxide (slaked 
lime): CaC 2 + 2H 2 O = C 2 H 2 -f- Ca(OH) 2 . In the presence of a 
suitable catalyst, acetylene combines with water to form acetaldehyde: 
C 2 H 2 + H 2 O = CHa CHO. The addition of hydrogen to acetalde- 
hyde, by catalytic hydrogenation or in other ways, yields ethyl alcohol, 
identical with the substance obtained from sugar; and the addition 
of oxygen to it, by a catalytic process or in other ways, yields acetic 
acid: CH 3 - CHO + 2H = CH 3 - CH 2 OH (ethyl alcohol); CH 8 
CHO + O = CH 3 COOH (acetic acid). These last two proc- 
esses are simple examples of very important general chemical changes, 
opposite in character and known as reduction and oxidation, re- 
spectively. 

Among many other types, organic bases are specially noteworthy. 
These may be depicted as derivatives of ammonia, NH 8 , simple ex- 



Chemistry 1 83 

amples being ethylamine, C 2 H 5 NH 2 , and aniline, C 6 H 5 NH 2 . 
Aniline is at the same time a derivative of the famous coal-tar hydro- 
carbon, benzene, C 6 H 6 , also found in some natural petroleums; and 
the mention of benzene opens out a great new vista of organic chem- 
istry, and brings us to Kekul's culminating vision. 

Although the innumerable army of the so-called "open-chain com- 
pounds" came into line with Kekule's original structural conception 
of 1858, yet benzene and its great array of associates (the so-called 
"aromatic compounds," because many of them had been discovered 
in aromatic plant products) remained in a camp apart. For several 
years Kekule failed to devise a structural formula for benzene which 
would harmonize his fundamental postulates with the extraordinary 
stability of the benzene system of six carbon and six hydrogen atoms. 
Then, in 1865, the flash of insight came to him at Ghent. In his 
own words: "I was sitting, writing at my textbook; but the work 
did not progress; my thoughts were elsewhere. I turned my chair to 
the fire and dozed. Again the atoms were gamboling before my 
eyes. This time the smaller groups kept modestly in the background. 
My mental eye, rendered more acute by repeated visions of the kind, 
could now distinguish larger structures, of manifold conformation: 
long rows, sometimes more closely fitted together; all twining and 
twisting in snakclike motion. But look! What was that? One of the 
snakes had seized hold of its own tail, and the form whirled mock- 
ingly before my eyes. As if by a flash of lightning I awoke; and this 
time also I spent the rest of the night in working out the conse- 
quences of the hypothesis." 

So arose, from this vision of the Ouroboros ("tail-eater") Serpenl 
(Fig. 11) of ancient Egypt and Greece, a symbol "half as old a< 
time," the conception of the "benzene ring," or closed chain, of si) 
carbon atoms: a fundamental idea which has been hailed as th< 
crowning achievement of the doctrine of the linking of carbon atom! 
(Fig. 12). It should be mentioned that the double bonds shown 
in Kekul6's benzene ring are much less reactive than those described 
above in open-chain systems; accordingly, benzene readily enters into 
substitution reactions. 

Meanwhile, Perkin (1838-1907), a young student at the Royal 
College of Chemistry in London, had prepared in the Easter vacation 



184 What Is Science? 




Pig. 11 The Ouroboros Serpent. The enclosed words, "the all is one," 
refer to the Platonic idea of the unity of matter. 

of 1856, "in my rough laboratory at home/' the first harbinger of 
thousands of coal-tar dyes, which became known as mauveine, or 
Perkin's Mauve. Through this discovery and the way in which he 
followed it up industrially, Perkin became the founder of pure and 

H 
/C 
HCX 

HC\ >^ 

\< 

H 

Fig. 12 The Benzene Ring. Kekule's original formula (left), with a 
later abbreviated representation. 

applied coal-tar chemistry. Benzene and a number of other closely 
related "primaries" found in coal tar, notably toluene (methyl-ben- 
zene), phenol (hydroxy-benzene), naphthalene, and anthracene 
(Fig. 13), gave birth to this great new field of organic chemistry. 

OH 





Toluene Phenol Naphthalene Anthracene 

CHa CeHs OH CioHg C^Hic 

Fig. 13 Formulae of some Coal-Tar Primaries. 



Chemistry 1 85 

Kekule's theory of the benzene ring came at the psychological 
moment; for it acted as the guiding principle in assiduous researches 
springing from Perkin's discovery and lasting even to the present day. 
Certain "primaries/' actually present in coal tar, are converted by 
chemical processes into "intermediates/' of which hundreds are now 
in common use. For example, benzene reacts with a mixture of nitric 
and sulphuric acids to give a monosubstitution product, nitrobenzene: 
C 6 Hfl + HNO 3 = H,O + C G H 5 NO 2 . Treatment with iron and 
hydrochloric acid (generating hydrogen), reduces nitrobenzene to 
aniline, one of the most useful "intermediates": C 6 H 5 NO 2 + 
6H = 2H 2 O + C H 5 NIL. By the application of further chemical 
processes to aniline and other "intermediates" it has proved possible 
to synthesize thousands of purely artificial dyes, drugs, photographic 
chemicals, perfumes, explosives, and fine chemicals in general. 
These developments, of such profound economic significance,. 
have all sprung from the test tubes and beakers in which Perkin 
then little more than a schoolboy prepared mauveine; and from 
Kekule's somewhat later vision of the snake biting its tail. 

At the present day, the hydrocarbons occurring so richly in nat- 
ural petroleums offer a somewhat similar growing-point in synthetic 
organic chemistry, leading to the so-called "petro-chemicals." 

In another sense the benzene ring opened the floodgates to a vast 
sea of other ring-systems, or cyclic molecular structures, which are no 
less numerous and important than open-chain structures. An almost 
unending variety of ring-systems is now known, containing from 
three to more than thirty atoms in the ring. These molecular ring- 
systems may be either homocyclic, consisting of carbon ring-atoms 
only, as in benzene and the structures of Fig. 13, or heterocyclic, 
containing other kinds of ring-atoms (notably nitrogen and oxygen) 
in association with carbon atoms, as exemplified in Fig. 14. 

Monocyclic systems (Fig. 14) contain one ring only in the mole- 
cule; polycyclic systems contain more than one, as in naphthalene 
and anthracene (Fig. 13). The different kinds of homocyclic and 
hctcrocyclic rings, joined together in many ways and numbers, give 
rise to multitudinous systems, each with its own series of derivatives. 
Moreover, there is no practical limit to the ways in which open-chain 
structures also may enter into molecules containing ring-systems. 



186 What Is Science? 

CH, 



HC CH 

II II 
HC CH 

\/ 
O 


HC CH 
HC CH 

Y 


HC CH 
HC CH 

\y 

NH 


HgC C/n2 

H 2 C CH 2 

\/ 
NH 


Furan 


Thioplien 


Pyrrole 


Piperidine 



Fig. 14 Some Simple (Monocyclic) Heterocyclic Systems. 

Such are the unending possibilities of the tangled molecular webs 
of the molecular world of organic chemistry, "built on a craftily 
complex plan, founded in deep simplicity." All life as we know it 
depends ultimately upon the startling and unique capacity of quad- 
rivalent carbon atoms to link together in rings and chains. 

Molecules of all grades of complexity are found among both nat- 
ural and artificial organic compounds. Natural organic molecules (a 
great many of which are also susceptible to artificial synthesis) 
range over a wide gamut of complexity, from those containing one or 
two carbon atoms (with their associated atoms of different kinds) to 
those containing thousands. On the whole, natural organic mole- 
cules tend toward complexity, as may be illustrated, for example, 
by glancing at the large natural groups of the carbohydrates, the 
plant and animal fats and oils, and the proteins. 

In the last analysis, the elaboration of all organic materials on the 
face of the earth depends upon the synthetic activities of the green 
leaves of plants, the tiny cells of which are the most efficient organic 
chemical laboratories in existence. It is in them that the initial syn- 
thetic operations are consummated. As the prophet Isaiah recognized 
long ago, "all flesh is grass/' The organic chemist might follow out 
this thought by exclaiming of nature: "What a tangled web she 
weaves, Starting in the cells of leaves!" 

Carbohydrates, and also proteins, function in building up the tissues 
of living organisms as well as in providing energy for their life proc- 
esses. Carbohydrates include sugars, starches, and celluloses, and are 
synthesized in plants from carbon dioxide and water through so-called 
photosynthetic processes initiated in the leaf in the presence of the 
green plant pigment and catalyst, chlorophyll, and fostered by the 



Chemistry 187 

radiant energy of sunlight. This energy enables the completely oxi- 
dized, or "burnt out," carbon and hydrogen in carbon dioxide and 
water to be largely deprived of their oxygen and built up into large 
molecules acting as storehouses of energy, such as glucose, CoHi 2 O 6r 
sucrose, Ci 2 H 2 2On, and starch, (C 6 H 10 O5) n . In further biochemical 
processes, still more oxygen is removed, and more energy stored up, 
in the constituents of fats and oils, such as triolein, CsTH^Oe, of 
olive oil. When such substances are slowly oxidized in the living 
organism, by uptake of atmospheric oxygen, they give up their stored 
energy, in the form of animal heat, muscular energy, etc., and revert, 
ultimately, to carbon dioxide and water. 

For example, the formation of 342 grams of ordinary sugar (sucrose) 
in the sugar cane or sugar beet, starting from atmospheric carbon 
dioxide and water, requires an intake of energy by the living plant 
equivalent to 1349.6 calories of heat; and this exact quantity of energy 
is released when the resulting sugar reverts completely by oxidation 
(whether slow or rapid) to carbon dioxide and water: Ci 2 H 2 2On + 
12O 2 = 12CO 2 + 11H 2 O + 1349.6 calories. 

This, in barest outline, is the natural carbon food cycle, shown 
diagrammatically in Fig. 15. There is also a nitrogen food cycle, 
in which the nitrogenous proteins, with molecular weights sometimes 
exceeding 100,000, are built up, and then degraded finally to carbon 



Animal assimilation 



ANIMAL CARBOHYDRATES 
AND FATS 

j [ Katabolic 
1 I change = 
\ \ oxidation, 
\\ energy 
\ \release 

Animal respiration^ 




PUNT CARBOHYDRATES 
AND FATS 



Photosynthesis: 
plant assimilation 



Fig. 15 The carbon food cycle. 



188 What Is Science? 

dioxide, water, and ammonia, with an accompanying uptake and re- 
lease of energy. 

The most concentrated form of organic energy is found in hydro- 
carbons. These occur notably in the enormous subterranean deposits 
of natural petroleum, which may have been formed in the course 
of geological ages from vast deposits of the remains of marine and 
swamp life, through their subjection to decomposition by various nat- 
ural agencies. When hydrocarbons are burnt in air, or vaporized and 
exploded with air (as in the internal combustion engine), two highly 
exothermic processes are concerned, namely, the oxidation of carbon 
and hydrogen to carbon dioxide and water, respectively. Conse- 
quently there ensues a copious liberation of energy in the form of 
heat. Now hydrocarbons are not assimilable, like carbohydrates, fats 
and proteins. Thus they cannot act as foods by delivering their 
stored energy to living organisms; but in such mixtures as natural 
gas, gasoline (petrol), kerosene, oil fuels, etc., derived from natural 
petroleums, they are used on a colossal scale through oxidation with 
atmospheric oxygen as sources of power for heating, lighting, and 
locomotion. 

The energy-content of certain specialized types of molecules finds 
a spectacular expression in organic explosives, such as nitroglycerine, 
CsHsOoNs; these have molecules containing much stored energy and 
capable of undergoing sudden intramolecular oxidation, started by 
shock or detonation, with the instantaneous generation of enormous 
volumes of gaseous products (carbon dioxide, steam, nitrogen, etc.) 
at very high temperatures. Under such conditions, liquid nitro- 
glycerine generates, in the twinkling of an eye, about 10,000 times 
its own volume of hot gases. 

Among the almost unending scries of natural organic compounds 
are pigments and dyes such as chlorophyll, hemoglobin, indigo, and 
alizarin; perfumes, occurring in the fragrant oils of plants and else- 
where; hormones (adrenaline, thyroxine, etc.); antibiotics (penicillin, 
etc.); alkaloids (strychnine, quinine, etc.); vitamins (ascorbic acid, 
etc.); and so on. The molecular constitutions of a great number of 
these have been determined; and as a rule this result has been fol- 
lowed in time by the artificial synthesis of the substance. One result 



Chemistry 1 89 

of this work has been to establish the prevalence of standard molec- 
ular patterns in natural organic products. Another outcome has 
been the possibility in many cases of modifying these natural pat- 
terns, and preparing simpler synthetic substances retaining the valu- 
able properties of the more complex natural ones. For example, the 
physiologically active fragment of the natural cocaine molecule reap- 
pears in the much simpler molecule of novocaine, a purely artificial 
substance which is much cheaper and in some respects even superior 
to natural cocaine. Work of this kind is leading to a rational system 
of therapeutics; but a great deal remains to be done in this direction. 

From what has been said it will be seen that much is now known 
of the general relationships existing between molecular structure and 
physiological action. To refer to a different field, a still more detailed 
correlation has been established between molecular structure, color, 
and dyeing properties. Thus, artificial dyes of manifold colors and 
shades, which nature never knew, have been synthesized by the 
thousand, mainly from constituents of coal tar. About half the dyes 
in common use are azo dyes, built up from coal-tar "intermediates." 
These owe their color to an unsaturatcd molecular unit, N = N , 
called the azo group; and many other so-called chromophores, or color- 
conferring groups, are known. In general, it is hardly possible to over- 
estimate the importance of molecular structure in organic chemistry. 

A very important growing-point of organic chemistry at present lies 
in the artificial production of materials composed of macromolecules, 
or molecules of very high molecular weights. These include a great 
variety of synthetic plastics, rubbers, fibers, etc. As a simple example, 
the gas ethylene, H 2 C = CH 2 , readily produced from ordinary alco- 
hol, is unsaturated, since the carbon atoms do not carry their full 
quota of hydrogen atoms. Under very high pressures, the ethylene 
molecules arc rearranged into bivalent ethylene units, CH 2 
CII 2 , and hundreds of these units then link together, end to end, 
to form the long-chain molecule of polythene, ( CH 2 CH 2 
CH 2 Clio CH 2 - CH 2 ), a waxlike plastic solid, used in a 
great variety of ways. 

The long threadlike macromolecule of natural rubber may be re- 
garded theoretically as composed of thousands of so-called isoprene 



190 What Is Science? 

units, C 5 H 8 , linked together in a regular head-to-tail sequence, the 
dotted lines showing their points of junction in the molecular frag- 
ment of the natural rubber hydrocarbon depicted below: 

etc. 4- CH, - C = CH - CH 2 - CH 2 - C = CH - CH* - etc. 
: i i 

CII 3 



Natural rubber has not been produced artificially; but many purely 
synthetic variants of the natural pattern are now manufactured ex- 
tensively, for example, neoprene, in which the methyl groups ( CH 3 ) 
of natural rubber are replaced by chlorine atoms ( Cl) : 

etc. Clio - C = CH - CH, 4- CHo C = CH - CII* 4- etc. 
i i 

Cl Cl 

Molecules of neoprene result through the ready spontaneous re- 
arrangement (compare ethylene, above) and coalescence of molecules 
of chloroprene, CH 2 = CC1 CH CH 2 , which is readily synthe- 
sized from acetylene. Such a coalescence of a number of like mole- 
cules to form a molecule of multiple molecular weight is called 
polymerization; the simple molecule is the monomer, and the multiple 
one the polymer. Macromolecules are often, but not always, produced 
by polymerization. 

Synthetic rubbers are not necessarily substitutes for natural rubber, 
as they show wide variations in physical properties, such as resistance 
to abrasion, oil, chemicals, and oxidation. They are built up in stages 
from simple organic substances, including acetylene, ethylene, alco- 
hol, and benzene. It should be added that macromolecules abound in 
nature, profoundly different types being represented, for example, 
by natural rubber, cellulose, and proteins, these last in such diverse 
forms as egg-white and silk. The purely artificial macromolecules of 
nylon are modeled structurally, with important variations, upon 
those of proteins. 

The complexity of organic chemistry is much enhanced by the 
fact that, as a consequence of work initiated by Pasteur in 1848, a 
"theory of molecular configuration" (or "space theory/' for short) was 
advanced in 1874 by the French chemist, Le Bel (1847-1930), and 
the Dutch chemist, van 't Hoff (1852-1911). In a beautiful and 



Chemistry 191 

classical research, at the very beginning of his scientific career, Pas- 
teur showed that tartaric acid can exist in distinct right- and left- 
handed forms, solutions of which turn the plane of a beam of polar- 
ized light in right- and left-handed directions, respectively. This is a 
refined physical distinction; the chemical properties of the two forms 
are identical. Later researches showed that many other organic com- 
pounds can exist in forms of this kind, one of the simplest of them 
being lactic acid, CH 3 -CH(OH)-COOH. 

It is a matter of common observation that many familiar objects, 
such as the hand, the foot, gloves, shoes, and spiral shells, can exist 
in right- and left-handed forms. They are said to be asymmetric, or 
devoid of symmetry. Indeed, all shaped objects fall into two classes, 
symmetric and asymmetric. A symmetric object, such as a teapot, 
gives an identical image in a looking glass; an asymmetric image 
gives a non-identical image, that of a right hand being a left hand. 
Only solid, three-dimensional, objects can exist in right and left 
forms. Consequently asymmetric molecules (and, by implication, 
molecules in general ) must be regarded as three-dimensional, and not 
flat, or two-dimensional. 

The space theory, which has been amply confirmed, replaces the 
flat structural formulae of Kekul6 by three-dimensional models, in 
which the four valencies of the carbon atom are directed toward the 
four corners of a regular tetrahedron (of which the carbon atom 
occupies the center), instead of toward the corners of a square. In 
terms of the later electronic theory of valency, the covalency is direc- 
tional (incidentally, the electrovalency is nondirectional). It follows 
from the space theory that the "natural angle" between any two 
covalencies of a carbon atom is the "tetrahedral angle" of 109 28" 
(Fig. 16). 

The tetrahedral model for methane is symmetric and therefore 
does not exist in right and left forms. If, however, the four atoms 
or groups attached to a carbon atom are of four different kinds the 
model becomes asymmetric. This condition holds for the lactic and 
tartaric acids, both of which exist in optically active forms, represent- 
ing right- and left-handed molecules, related as object and non- 
identical image, as shown below in the space formulae, or molecular 
configurations, for the two forms of lactic acid (Fig. 17). The carbon 



192 What Is Science? 




H 



H 



(A) <B) 

Fig. 16 Methane, CH 4 : after (A) Kekule, (B) Le Bel and van f t Hoff. 

atom attached to four different kinds of groups, known as an asym- 
metric carbon atom, is situated at the middle of each diagram, and 
the arrows represent the opposed directions of rotation of polarized 
light. 




COOH 




COOH 



Fig. 17 Molecular configuration of the optically active lactic acids. 



The tetrahedral angle is preserved in general, so as to minimize 
strain in organic molecules: for instance, in the symmetrical paraffin 
hydrocarbons the chains of carbon atoms take up a zigzag conforma- 
tion instead of assuming Kekule's plane rectilinear disposition. Simi- 
larly, large ring-systems undergo buckling or folding into multiplanar 
conformations, so as to maintain the tetrahedral angle and avoid the 
production of strain. Considerable strain is unavoidable, however, in 
double and triple bonds and three- and four-membered ring-systems. 

Most of the simpler organic compounds have symmetric molecules; 
but asymmetry is very common in the more complex ones. In partic- 



Chemistry 1 93 

ular, the great mass of the organic material of plants and animals is 
asymmetric and optically active. 

For ordinary purposes the flat Kekulcan formulae are still in gen- 
eral use; but for the finer aspects of organic chemistry, especially in 
the borderland with biochemistry (which itself may be regarded as 
an outgrowth of organic chemistry), it is becoming increasingly nec- 
essary to refer to the fuller spatial interpretation of the organic mole- 
cule, seeing that, for example, the right- and left-handed forms of the 
same substance often differ profoundly in their physiological action. 
This is a result of the asymmetry of the constituents of living matter. 
As Pasteur wrote in 1860: "If the mysterious influence to which the 
asymmetry of natural products is due should change its sense of 
direction, the constitutive elements of all living beings would assume 
the opposite asymmetry. Perhaps a new world would present itself 
to our view. Who could foresee the organization of living things if 
cellulose, right as it is, became left; if the albumin of the blood, 
now left, became right? These are mysteries which furnish much 
work for the future, and demand henceforth the most serious consid- 
eration from science/' 

Pasteur (1822-1895), a child of humble parents who became 
one of the greatest of all Frenchmen, has been described as "the 
most perfect man who has ever entered the kingdom of science"; he 
was also one of the most versatile in the range of his researches. His 
foundation of the subscicnce of STEREOCHEMISTRY, or chemistry in 
space, which now permeates the whole vast realm of the organic 
world, was but the first episode in a scientific career of unsurpassed 
brilliance. The space theory, arising from his first research, does not 
supplant Kekule's ideas. Rather, this theory (1874) supplements that 
of molecular structure (1858), by extending the molecule from two 
dimensions into three: in Tennyson's words: "Science moves, but 
slowly slowly, creeping on from point to point." 

During the present century, however, the advance of chemistry, as 
of science in general, has become increasingly rapid, in a kind of 
geometrical progression. Techniques have increased in number and 
subtlety, keeping pace with theoretical ideas which have grown con- 
stantly in refinement and complexity. The brilliant amateur, and the 
old-fashioned natural philosopher who took all natural knowledge 



194 What Is Science? 

for his province, have alike disappeared, to be replaced by profes- 
sional scientists with highly specialized interests, knowledge, and out- 
look. At the same time the literature of scientific publications has 
become so vast as to threaten to engulf those whose work it records. 
The material achievements of modern chemistry, accomplished by 
an ever-increasing army of workers, are astounding; but, more than 
this, the intimate chemical and physical knowledge that man has 
now acquired of his terrestrial environment represents the greatest 
of all his intellectual achievements; and this triumph of mind over 
matter is rendered even more complete by the proof that the unity 
of matter is universal, extending to the planets, stars, and nebulae. 
Science moves ever onward, and cannot "stand at gaze, like Joshua's 
moon in Ajalon." It rests with the moral and political leaders of man 
to see that science is applied in his service and not misapplied in 
his disservice: herein lies the greatest problem of civilization today. 
Man must learn to master and control himself as he has learned to 
master and control nature. 

This brief survey of a vast subject may end aptly in some words 
written long ago by Lucretius, in the first century B.C.: "Practice, 
together with the acquired knowledge of the untiring mind, taught 
men by slow degrees, as they advanced on their way step by step. 
Thus time by degrees brings each several thing forth before men's 
eyes, and reason raises it up into the borders of light; for things must 
be brought to light one after the other, and in due order in the 
different arts, until these have reached their highest point of develop- 
ment/' 



infeiemenffti. forty Bf4njt. 



Seutr. A 
tuff. A 
fflWfar.^7 



<su. (D 

SReratr. S 



The Four Elements and the Three Principles. 



BIOCHEMISTRY 



ERNEST BALDWIN 



about 

Ernest Baldwin 



Ernest Baldwin was born at Gloucester, England, in 1909 and after 
attending local schools took his bachelor s degree at St. Johns College, 
Cambridge. Further studies, with emphasis on biochemistry, gained 
him a Ph.D. degree from Cambridge University in 1934. From 1936 
to 1943 he was a university demonstrator in biochemistry at Cam- 
bridge, and then university lecturer until 1949. His present position is 
professor of biochemistry, University College, London, an appoint- 
ment which he has held since J950. The main lines of Dr. Baldwin s 
researches have been in the fields of biochemical evolution and 
comparative biochemistry. Besides conducting investigations at Cam- 
bridge and the University of London, he has pursued his scientific 
work as a guest worker at the Marine Biological Laboratories in Plym- 
outh, England, at several stations in France and, in 1948, at Woods 
Hole, Massachusetts. In addition to a large number of research papers 
and review articles he has written two standard works, An Introduc- 
tion to Comparative Biochemistry, an admirable little primer now in 
its third edition, and Dynamic Aspects of Biochemistry, regarded as a 
landmark in its field. 

Dr. Baldwin has been married for 22 years and has two children, 
a daughter, Nicola, age 17, and a son Nigel St. John, age 15. He writes, 
"I am not interested in politics except insofar as they affect income tax 
and similar unpleasant phenomena, but outside biochemistry I find a 
great deal of pleasure in music, particularly Bach and thereafter up to 

196 



about Ernest Baldwin 197 

the period of Debussy and Ravel. I make no claim either to like or 
understand the majority of contemporary composers. I cant sing or 
paint or speak foreign languages with any fluency, but I do get a good 
deal of pleasure out of playing the piano with much verve and little 
accuracy. I am a confirmed pipe smoker of long standing and, like Dr. 
Johnson, I love to invigorate myself with wine but abhor drunken- 
ness. I can think of only one other interest that might be mentioned 
and that is that, since my family moved recently to a new house after 
living for some years in a London flat, I find myself developing a keen 
interest in gardening." 



BIOCHEMISTRY 

ERNEST BALDWIN 



Introduction 

The use of chemical tests as an aid to the diagnosis of various dis- 
eases formed the foundations upon which the science of biochemistry 
came afterward to be built. The detection of "sugar" in urine and 
that of protein in urine are still among those used as aids to the 
diagnosis of diabetes and certain forms of kidney disease, but physio- 
logical chemistry, as it was formerly called, saw wider fields for the 
application of chemical methods to biological problems. In the 
course of time biochemistry, as we know it today, grew up and de- 
veloped as an independent discipline of which physiological chemis- 
try is now only a comparatively small part. Living matter of any and 
every kind offers a proper field for biochemical study, and of the 
academic and, indeed, the economic value of its discoveries there can 
be no doubt whatsoever. 1 

The study of living things began with the observation of objects 
visible to the naked eye and was later carried downward to more 
intimate levels by dissection and, later still, by microscopy. Eventually 
however further exploration of the fine details of morphological struc- 
ture became restricted by the purely physical limits of resolution of 
the ordinary optical microscope. Even the most recent developments 

1 The reader can get some idea of the wide range and variety of subjects covered 
by present-day biochemistry if he will glance at the section headings of this essay. 

198 



Biochemistry 199 

in microscopy have pushed the limits of resolution very little further, 
although newer devices, especially the electron and "flying-spot" micro- 
scopes, show great promise for the future. In the meantime biochem- 
istry has added much to the methods available for the study of bio- 
logical objects and phenomena. Starting from the level of atoms and 
molecules it has been the biochemists' business to work upward, 
through large and complex molecules to progressively larger and 
more complicated systems, until in the end this "upward from be- 
low" line of progress meets that of "downward from above." Already, 
in fact, certain subcellular particles, known to microscopists as mito- 
chondria, have become a favorite material for biochemical study. 

Like other branches of biology, biochemistry can be considered as 
divisible into two main branches. There is first of all the problem of 
the chemical composition of living stuff, corresponding to the struc- 
tural, morphological or "static" approach which, in the end, amounts 
to a very specialized kind of organic chemistry. It is the second, the 
physiological and essentially dynamic approach, that is most charac- 
teristic of biochemistry today; the primary question has shifted from 
"what is it made of?" to "how does it work?" 

As a result of study along both these lines, studies embracing ani- 
mals, plants, bacteria, protozoa, fungi and so on, it has been found 
that living organisms of every kind have a great deal in common. 
Among animals, for example, the over-all chemical composition and 
the general chemical dynamics are remarkably similar. Admittedly 
there are differences between different types and groups of animals, 
but the most striking fact of all is not that there are differences, but 
rather that there are not more of them. 

More is known about the biochemistry of animals than of any 
other group of living things and, since in an article of this kind the 
material selected for discussion can necessarily be only a fragment of 
all that is available for consideration, the main emphasis here will 
be placed upon the biochemistry of animals. 

Metabolism 

From the structural viewpoint it can be said that living stuff is com- 
posed chiefly of water and small amounts of simple inorganic salts, 



200 What Is Science? 

and that the predominant organic constituents are proteins, lipids 
(fats) and carbohydrates all relatively complex substances as judged 
from the point of view of classical organic chemistry. The chemical 
changes that go on within the structural framework of the living cell 
are characterized by the fact that they proceed far more rapidly in 
the cell itself than they do when the reactants are taken together in a 
test tube or a flask. The familiar sugar glucose, for example, is a very 
stable substance, even in aqueous solution, provided that it is kept 
under sterile conditions, but if living yeast cells have access to it the 
sugar is very rapidly decomposed with production of alcohol and 
carbon dioxide. Other microorganisms similarly attack glucose, rap- 
idly and with production of other and different products. 

The sum total of all the chemical reactions taking place in a living 
system collectively make up its metabolism and can be classified un- 
der two broad headings, first katabolic or breakdown processes, which 
involve the chemical degradation of complex substances into simpler 
materials, especially carbon dioxide and water. These katabolic 
changes provide the energy which is expended in muscular move- 
ment, heat production and other forms of what we may call "bio- 
logical work." They also furnish energy for processes of the second, 
or anabolic kind; these are essentially energy-consuming and syn- 
thetic in character and play a part, for example, in the storage of 
foodstuffs in the tissues. Glucose, to take a specific example, is a 
fairly simple chemical substance which can be built up by an energy- 
consuming process into the complex polysaccharide glycogen and is 
stored in that form in the liver and muscles of animals. Very similar 
processes are involved in the production of starch, the chief storage 
polysaccharide of many plants. Glycogen and starch alike are ex- 
tremely complicated substances and both are built up by the chem- 
ical union of large numbers of glucose molecules. Other anabolic 
changes are concerned in the production of new tissue material in 
growing organisms, and in the continued formation in the adult of 
numerous specialized substances such as hormones, pigments, en- 
zymes and the like, quite apart from making good the general wear 
and tear of everyday life, e.g., by producing expendable materials 
such as hair, nails and skin. 



Biochemistry 201 



Enzymes 



Metabolic changes, anabolic and katabolic alike, can proceed as fast 
as they do in living cells only because they are catalyzed by the en- 
tities known to the biochemist as enzymes. An enzyme is a biological 
catalyst, i.e., an agent which accelerates some particular chemical 
change, and, although it participates in some way in the reaction it 
influences, is regenerated at the end of the reaction and so can be 
used over and over again. Very few metabolic reactions proceed at a 
detectable speed in the absence of the appropriate enzyme and yet 
the total number of reactions taking place in even a comparatively 
simple cell such as yeast is very large, from which it follows that the 
total number of enzymes is also exceedingly large. 

A considerable number of enzymes have been isolated in the pure 
state and shown to be proteins. Sometimes, and notably among en- 
zymes concerned with biological oxidation reactions, there is at- 
tached to the protein a specialized nonprotein moiety known as a 
prosthetic group and, in all such cases about which we have informa- 
tion, this prosthetic group plays a leading part in the reaction which 
the enzyme catalyzes. This point may become clearer if the reader is 
reminded of hemoglobin, the red coloring matter of blood. This con- 
sists of a protein, globin, to which is attached a prosthetic group 
known as heme, and it is to this prosthetic group that the oxygen is 
attached which the hemoglobin carries from the lungs to the tissues 
that require it. 

These enzymic catalysts form the groundwork upon which all dy- 
namic intraccllular events arc organized. These include a great vari- 
ety of energy-yielding processes, such as the katabolism of fats and 
carbohydrates, and numerous synthetic operations which produce 
proteins and innumerable other important substances such as en- 
zymes themselves, together with hormones, pigments and so on. For 
two decades or more research was largely concentrated upon the de- 
tailed study of individual enzymes and the particular reactions they 
catalyze, but more recently it has become not only possible and de- 
sirable but even fashionable to study them in groups and systems. 



202 What Is Science? 

Many of these systems are extremely complex, and involve not 
only the enzymes themselves but in addition a larger or smaller num- 
ber of accessory cof actors. These cof actors, or coenzymes as they are 
usually called, are required in some cases because they are, in effect, 
parts of the enzymes themselves, in others because they participate in 
the reaction or reactions undergoing catalysis. The nature of these 
cofactors varies over a wide range of chemical types; but one simple 
example will perhaps illustrate and clarify the point. Saliva contains 
a powerful starch-digesting enzyme called salivary amylase and this 
plays an important part in the digestion of starchy foodstuffs. If, 
however, saliva is freed from chlorides, which is easily enough done 
in the laboratory, it loses its starch-splitting properties. These proper- 
ties are promptly restored however if a little common salt (sodium 
chloride) is added to the solution: chloride is, in fact, the cof actor of 
salivary amylase. 

Perhaps the most characteristic features of enzymes as a whole are 
their susceptibility to heat and their extremely high specificity. A few 
minutes heating to 100C suffices to inactivate completely the major- 
ity of enzymes. With regard to specificity, various degrees of "exclu- 
siveness" can be recognized, but as a rule (and in this respect these 
biological catalysts differ markedly from such familiar laboratory cata- 
lysts as platinum black) one enzyme can catalyze one chemical reac- 
tion and one only. Practically every reaction going on in a living cell 
has its own particular, specific enzyme, but the reader must not pic- 
ture the cell as a mere bag full of enzymes, for these catalysts are 
organized into teams or systems, each team carrying out some par- 
ticular part or parts of the whole metabolism of the cell and being 
geared up to other teams. Every sort of chemical transformation go- 
ing on in a cell is, in fact, more or less immediately associated with 
all the rest. 

The chief classes of enzymes are (a) those which catalyze proc- 
esses of hydrolysis, i.e., processes in which a given substance is split 
by means of water, for example. 

cane sugar -f water = glucose + fructose 

All of the enzymes concerned with digestion belong to this group. A 
second group (b) catalyzes the transference of some given chemical 



Biochemistry 203 

grouping or radical from one substance to another. A particularly 
large and important subgroup of transferring enzymes is that in- 
volved in biological oxidations. In this case the radical transferred 
consists of a pair of hydrogen atoms and these are transferred from 
the substance undergoing oxidation to an appropriate "hydrogen ac- 
ceptor/' Often this hydrogen acceptor is a coenzyme and one exam- 
ple of this sort is catalyzed by an enzyme called lactic dehydrogenase. 
It can be represented thus: 

CH 3 CII(OH)COOH+cocnzyme-CII 3 CO.COOH+coenzyme-2H 

(lactic acid) (pyruvic acid) 

A third group (c) catalyzes isomerization, i.e., the rearrangement 
within a molecule of its constituent atoms. 



Digestion 

Normally, although enzymes can usually be separated from the tis- 
sues within which they discharge their biological functions and can 
be studied individually, they act in nature in an organized manner. 
In the processes of digestion, for example, the food material is sub- 
mitted to the action of a series of hydrolytic enzymes as it passes 
along the alimentary canal from mouth to anus. Each of these diges- 
tive enzymes individually can catalyze one particular step or one small 
group of similar steps in digestive hydrolysis, but digestion does not 
proceed in a series of discrete steps or stages; it is, rather, an organ- 
ized procession of chemical events, the products of activity of one 
enzyme becoming the substrate of the next enzyme in the chain. All 
the enzymes concerned in digestion are members of the class of "hy- 
drolases." 

The over-all result of digestion is that the complex molecules mak- 
ing up the food are broken down into their chemically simpler con- 
stituent materials, a necessary preliminary to their absorption by the 
digestive tract. For instance, the large, complex molecules of starch 
and glycogen are broken down into molecules of the simple sugar 
glucose, a process in which several enzymes are concerned, viz., sali- 
vary amylase, a similar amylase produced by the pancreas, and the 



204 What Is Science? 

intestinal enzyme maltase. The two amylases break down starch into 
maltose, the molecule of which is only twice the size of that of glu- 
cose. Even so, maltose cannot be absorbed as such and its formation 
is followed by its decomposition into glucose by the enzyme maltase. 

Proteins similarly are chemically dismantled and in this case the 
final products of digestion are comparatively simple substances known 
as ammo acids. This time an even larger number of enzymes are in- 
volved, including the pepsin of gastric juice, trypsin and chymotrypsin, 
contributed by the pancreas, and a large number of other enzymes 
known as peptidases which arise partly in the pancreatic juice and 
mainly in intestinal secretions. 

It is mainly in the form, therefore, of comparatively small and 
chemically simple molecules that the food of an organism is actually 
absorbed into the body, passing through the wall of the intestine, 
entering the blood or the lymph and being distributed thereby to 
the body as a whole. 



Storage of Fat and Carbohydrate 

Fats and carbohydrates can be stored in the body, the former to an 
almost unlimited extent, as witness the professional "fat men" whose 
fat-storing prowess can be appraised at most fairs and side shows for 
a modest charge. Carbohydrate material is stored in the form of gly- 
cogen, the principal storage house for which is the liver, but the ca- 
pacity of the latter is limited. Carbohydrate can also be stored, 
though again to a limited extent and again in the form of glycogcn, 
in the muscles, but if more carbohydrate material is ingested than can 
be accommodated in the storage space available, the excess is trans- 
formed into fat and deposited in the fat depots of the body. 

The nature of the fat present in these depots is, chemically speak- 
ing, exceedingly complicated, for part is derived directly from the 
food fat and part by the transformation into fat of excess carbohy- 
drate, so that the nature but not the quantity of the depot fat is 
open to modification by the nature of the food fat. The amount of 
fat stored is influenced however by the amount of carbohydrate con- 
sumed, even if no fat at all is eaten. The acquisition of a slim figure 



Biochemistry 205 

means deprivation of starchy as well as fatty foods, and even proteins 
must be kept to a low level. 

The reserves of carbohydrate on the other hand consist entirely of 
glycogen, a polysaccharide that is built up exclusively from glucose 
and resembles the more familiar starch in many respects. Glycogen is 
the hub about which the wheel of carbohydrate metabolism revolves 
in the animal kingdom; polysaccharides containing sugars other than 
glucose play important parts in the storage and metabolism of carbo- 
hydrate material in plants, but have little or nothing to do in ani- 
mals. Being formed as it is entirely of glucose units, the composition 
of glycogen is not influenced by the nature of the carbohydrates in- 
gested. The main product of the digestion of a carbohydrate meal 
is, as has already been mentioned, glucose itself, which can yield 
glycogen directly, but appreciable quantities of certain other sugars 
are also produced, absorbed and subsequently transformed into glu- 
cose and in this way also contribute to the synthesis of glycogen. 



Function and Metabolism of Protein Foods 

Proteins are built up entirely from amino acids. The latter are rela- 
tively simple, nitrogen-containing substances which behave both as 
acids and as bases at one and the same time. Proteins are built up 
from large numbers of these amino-acid units, the acidic group of 
one being united with the basic group of another. The resulting long 
chains of amino-acid units can assume a great variety of forms; some- 
times they are exceedingly insoluble and aggregate together to form 
skin and hair; some have catalytic properties and are, in fact, enzymes; 
in others again the chain becomes coiled up to form virtually struc- 
tureless, soluble molecules like those of egg white (egg albumin). 

Unlike fats and carbohydrates, proteins and the products of their 
digestive breakdown, the amino acids, are not stored in the body to 
any great extent except during periods of tissue growth, e.g., during 
pregnancy and childhood or during convalescence after a wasting ill- 
ness; in these exceptional cases, new tissue proteins are being laid 
down and amino acids are accordingly retained for their formation. 
Now proteins have a unique importance in that they are the body's 



206 What Is Science? 

principal source of nitrogen, which is of enormous importance in the 
animal body, entering into the composition not only of proteins but 
of many other substances as well. Even during periods of protein de- 
privation, and even indeed during total starvation, small amounts of 
nitrogenous substances are excreted in the urine. This nitrogen arises 
from metabolism of proteins and amino acids in the body, metabo- 
lism which still goes on so long as the animal is alive at all. If nitro- 
gen thus wasted is not replaced, the nitrogen necessary for mainte- 
nance of the essential processes of keeping alive is found by breaking 
down some of the proteins of the tissues, especially those of the mus- 
cles, and it follows that an adequate supply of protein must always 
be included in the diet if loss of weight, emaciation and eventual 
death are not to result. 

The question of adequacy has been much discussed in the past and 
is an important problem of rationing in times of war and famine. If 
too little protein is consumed the organism loses more nitrogen than 
it gains, and makes good the over-all deficit by breaking down its own 
tissues. If input is equal to output, however, a state known as nitro- 
genous equilibrium is attained, and much work has gone into determi- 
nations of the quantity and quality of protein food required just to 
maintain this condition of equilibrium. According to the classical 
work of the German nutritionist Rubner and his associates, some- 
thing of the order of 100 gm of mixed protein is required daily, but 
in later experiments on himself Chittenden, an American biochem- 
ist, found that he could keep himself in equilibrium on only 30-35 
gm protein daily and, moreover, his health improved during the pe- 
riod of the experiments. But the disparity between these estimates 
does not reflect differences in individual requirements but differences 
rather in the nutritional value of the different proteins. 

The essential function of protein food is that of supplying the ani- 
mal with certain particular amino acids. Altogether some 20-25 dif- 
ferent chemical species of amino acids are known to occur in proteins 
and of these the animal body can synthesize some by its own re- 
sources even if its diet does not contain them, but there remain 
some ten or a dozen which are said to be "essential"; essential be- 
cause, although they enter into its structure and metabolism, the 
animal cannot synthesize them for itself and has perforce to rely on 



Biochemistry 207 

its food proteins. The list of essential amino acids includes such sub- 
stances as histidine, lysine and tryptophan, some of the more complex 
members of the amino-acid family (see Fig. 1). If nitrogenous equi- 
librium is to be maintained, therefore, the dietary protein must sup- 
ply enough of each and every one of those amino acids that are es- 
sential. But proteins vary widely in chemical composition as far as 
their amino-acid constituents are concerned, and it is worthy of men- 
tion that certain plant proteins are totally devoid of certain of the 
essential amino acids, notably the maize protein, zein. This protein 
contains no tryptophan and no lysine, both of which figure on the 
list of essential amino acids, and consequently, if zein were the only 
protein present in the diet, nitrogenous equilibrium could never be 
attained, no matter how much might be consumed. Some classical 
experiments carried out by the American biochemists Osborne and 
Mendel showed that if young rats were kept on diets of which zein 
formed the sole protein, they lost weight and would have died if the 

NON-ESSENTIAL ESSENTIAL 

CH 2 (NII 2 )COOH y\ . CH 2 CH(NH 2 )COOH 

glycine |l I i tryptophan 

CH 3 CH(NH 2 )COOH ^H NH 2 

alanine ' 



COOH ! 

I *->H 2 

CH 2 I 

i <^tt 2 

<,NH,,OOOH 

lysine 

Fig. 1 Formulae of some amino acids. 

experiment were continued. If tryptophan were added to the diet the 
animals maintained their weight but failed to grow, and only when 
the other missing amino acid, lysine, was also provided was there any 
resumption of normal growth. 

Generally speaking, animal proteins such as are present in meat, 
fish, eggs, cheese and milk are much richer in essential amino acids 



208 What Is Science? 

and are therefore of higher nutritional value than are plant proteins. 
Correspondingly less animal protein need therefore be consumed for 
the maintenance of nitrogenous equilibrium than if the food con- 
sists mainly of cereals and pulse. In Chittendcn's experiments animal 
proteins of high nutritional value were used exclusively whereas, in 
the older work of the Rubner school, where a mixture of plant and 
animal proteins was taken, a three times larger total protein intake 
was required to attain the equilibrium condition. 

The primary and essential function of protein foodstuffs is, then, 
that of providing a sufficiency of all the essential amino acids re- 
quired for the maintenance of body structure and of the body ma- 
chinery. Indeed, protein food can be totally replaced by mixtures of 
purified amino acids. This has been done in experiments on dogs 
and on groups of medical students, none of which experienced any 
untoward consequences as a result. When, however, the essential 
amino acids are taken in the form of protein, the essential com- 
ponents are invariably accompanied by relatively large quantities of 
non-essential amino acids, such as glycine and alanine. In any case 
the vast majority of human beings take considerably more protein 
than the minimum necessary for the maintenance of nitrogenous 
equilibrium, so that in either case a larger or smaller surplus of amino- 
acid material remains when the immediate requirements of the tissues 
have been satisfied. The surplus amino acids are not wasted; instead 
they undergo chemical manipulations which divert them into the 
pathways of carbohydrate and fat metabolism. Some contribute to 
the carbohydrate stores and are accordingly said to be glucogcnic; 
others, which give rise to fats, are said to be ketogcnic. It is thus 
possible to lay down fat or glycogen in an animal by feeding massive 
meals consisting wholly of protein. 

We have already noted the inability of the animal body to store 
amino acids or proteins as such. Any amino acids over and above the 
amount required to satisfy the immediate needs of the tissues arc 
treated as surplus material. The nitrogenous part of the molecules is 
removed and excreted, and it is from the residual nitrogcn-frcc mate- 
rials, known as a-keto-acids, that new fat and new carbohydrate are 
elaborated. 

The removal of the nitrcgen-containing part of the molecule is 



Biochemistry 209 

known as deamination and is catalyzed by means of a transferring 
enzyme. A superfluous amino-acid molecule reacts with a-ketoglu- 
taric acid (see Fig. 2). The latter, which arises in the normal course 
of carbohydrate metabolism, takes over the nitrogenous part of the 
molecule so that the latter becomes an a-keto-acid available for 
conversion into fat or carbohydrate, while the a-ketoglutaric acid is 
converted into glutamic acid. Subsequent further reactions detach 
the nitrogenous radical from this glutamic acid so that a-ketoglutaric 
acid is regenerated and can be used all over again. 

Starting with surplus amino acids, then, we arrive at two new sets 
of products: first the a-keto-acids which contribute to the fat and 
carbohydrate stores of the body, while the second product consists of 
the nitrogen-containing groups of glutamic acid molecules. These 
groups, as has been said, are removed and subsequently excreted. In 
some animals they are split off and excreted in the form of am- 
monia; in others they are put through a series of anabolic reactions 
leading to the formation of urea, which is excreted as such; in yet 
others a different series of anabolic processes leads to the formation 
and excretion of uric acid. These points are summarized in Fig. 2. 

Carbohydrate metabolism 

* 
Surplus amino acids ^ ^. . kttoglutaric acid 

"Nitrogen 

containing 

groups 



a Keto-acids -*-^ ^*-- glutamic acid 
Fig. 2 To illustrate deamination and formation of excretory products. 

The excretion of ammonia is characteristic of aquatic animals as a 
whole. These creatures enjoy an abundant supply of water which 
can flush away ammonia from the blood as fast as it is formed. Now 
ammonia is a very toxic material; it is lethal to rabbits, for example, 
at a concentration of only 1 part in 10,000 parts of blood. Urea 
and uric acid, by contrast with ammonia, are comparatively innoc- 
uous, and in terrestrial animals, whose water supply is usually more 
or less seriously restricted, the clangers of ammonia poisoning are 
evaded by the production, not now of ammonia, but of urea (in 






210 What Is Science? 

mammals and amphibia) or of uric acid (in birds, snakes and liz- 
ards). This is an interesting example of biochemical adaptation to 
environmental conditions. 



Metabolism of Fat and Carbohydrate 

Fats and carbohydrates, together with surplus proteins, are mainly of 
importance as energy-yielding materials or "fuel," and in the ordinary 
course of events the energy requirements of the body are met by 
the "combustion" of a mixture of fat and carbohydrate. In normal 
individuals metabolism proceeds smoothly enough, but in certain 
diseases, notably diabetes, there is a breakdown in the normal balance 
between carbohydrate and fat metabolism and much has been 
learned about normal metabolism by studying these abnormalities. 

The carbohydrate requirements of the tissues are met by glucose 
carried in the blood. This arises from glycogen stored in the liver. 
Normally the concentration of glucose in the blood is approximately 
1 gm per liter and in the normal, healthy adult varies within very 
narrow limits. This normal, steady level is maintained by balancing 
the formation of glucose from glycogen (glycogenolysis) against its 
absorption by other tissues, and both these processes are under hor- 
monal control. Adrenalin (epinephrine), for instance, provokes a rise 
in the level of blood glucose, as happens under conditions of emo- 
tional stress, but this is only a short-term emergency reaction. At 
ordinary times and in normal individuals the long-term balance is 
held by the antagonistic action of two other hormones, insulin, se- 
creted by the islet cells of the pancreas, and a so-called diabctogenic 
hormone produced by the anterior part of the pituitary gland. 

In diabetes the blood glucose rises to very high levels, partly be- 
cause of overproduction by glycogenolysis and partly because of the 
impaired power of the liver to manufacture glycogen from it. In- 
jections of insulin correct this symptom and do so by encouraging 
the storage of glucose in the liver in the form of its polymer, gly- 
cogen. The diabetogenic hormone has precisely the opposite effects. 
If administered to normal individuals, it encourages glycogenolysis 
and discourages glycogen formation and storage, and it is by balanc- 



Biochemistry 211 

ing the effects of these two hormones one against the other that the 
level of blood glucose is regulated in normal individuals. Carbohy- 
concentrations of these two hormones rather than by the absolute 
drate metabolism, therefore, is controlled by the ratio between the 
amounts of either. The characteristically high level of blood glucose 
found in diabetes is commonly due to deficiency of insulin produc- 
tion, but can be due equally to overproduction of the diabetogenic 
hormone. Whichever is the case, the injection of insulin, either by 
remedying a deficiency of insulin formation or by counteracting an 
overproduction of diabetogenic hormone, can bring the blood sugar 
to a normal level and restore normality of carbohydrate metabolism 
in general. 

The presence of abnormally large concentrations of glucose in the 
blood of diabetic subjects is the reason for what is perhaps the best 
known symptom of this disease, the presence of "sugar" in the urine. 
This is because the kidneys have only a very limited power of holding 
back glucose and, when excessive quantities are present in the blood, 
are unable to retain the excess. 

In itself the excretion of glucose in the urine is wasteful of glucose, 
which is an important fuel material, and is highly inconvenient be- 
cause its excretion is attended by the formation of large volumes of 
urine, which leads in its turn to a correspondingly intense thirst. 
Nevertheless, glycosuria as such is not particularly harmful, but as- 
sociated with it is another urinary abnormality known as ketonuria, 
a consequence this time of the derangement not of carbohydrate but 
of fat metabolism. 

The katabolic breakdown of the body fats results in the formation 
of large numbers of small fragments, each of which contains only 
two carbon atoms. Normally these fragments are completely oxidized 
to carbon dioxide and water, but their oxidation is dependent upon a 
concomitant metabolism of carbohydrate. Now in diabetes, carbohy- 
drate metabolism is subnormal and the 2-carbon fragments cannot 
be oxidized as fast as they are formed; instead they tend to ac- 
cumulate and are diverted along an alternative pathway. Pairs of 
2-carbon units unite under these conditions to give a group of 
substances known collectively as ketone bodies, viz., acetoacetic and 
0-hydroxybutyric acids, together with traces of acetone. All three of 



212 What Is Science? 

these are rather toxic compounds, quite apart from the fact that 
two of them are acids, and the accumulation of these in the blood 
is largely responsible for the dangerous clinical factors in un- 
treated diabetes. The rise in concentration of these ketone bodies 
results in their appearance, together with that of glucose, in the 
urine of untreated diabetics. 

Important evidence regarding the normal lines of metabolism has 
thus been obtained by experimental studies of diabetic subjects and 
we can now return to consider some of the main lines of metabolism 
in normal animals. The formation of 2-carbon fragments from fatty 
acids is a somewhat complicated operation involving a considerable 
number of chemical reactions which need not be considered here in 
detail. The same is true of the breakdown of glucose and glycogen, 
which yields as an important intermediary product a simple com- 
pound, pyruvic acid which contains three carbon atoms. These and 
certain other facts already mentioned concerning the metabolism of 
amino acids can be summarized diagrammatically as in Fig. 3 for the 
purposes of the rest of our discussion. 

PROTEINS 

t 

CARBOHYDRATES ^ _J1 Pyruvate < Amino acids 



I 



FATS ^ 1 Acetyl-coenzyme A 



I 



Carbon dioxide 
Fig. 3 Summary of some main lines of metabolism. 

Ultimately, as the diagram indicates, all three of the main classes 
of food stufts are converted into a common intermediary, viz., a 
derivative of the 2-carbon substance known as acctyl-cocn/ymc A, 
and are oxidized away along a common pathway. Pyruvate, arising 
from glucose and glycogen by a process known as glycolysis, loses 
one carbon atom as carbon dioxide and yields acetyl-cocnzymc A. 
Glucogenic amino acids yield pyruvate, for it is at this point that 
their metabolic pathway joins that of carbohydrate, and hence give 
rise to acetyl-coenzyme A. Ketogenic amino acids also yield acetyl- 



Biochemistry 213 

coenzyme A, this time more directly, and join the pathway of fat 
metabolism at this point. 

It is worth noticing, before we go further, that carbohydrate can 
be and indeed is synthesized from pyruvate, and fat from acetyl- 
coenzyme A (dotted arrows in diagram), but once the step leading 
from pyruvate to acetyl-coenzyme A has been traversed, no reversal 
is possible under the conditions that obtain in animal tissues. Con- 
sequently, while carbohydrate can be converted into fat, fat is not 
convertible into carbohydrate. Protein, however, can give rise to both 
carbohydrate and fat. 



The Citric-Acid Cycle 

The discovery of the nature of the common oxidative pathway and 
that of the mechanisms involved was due largely to H. A. Krebs, 
a Nobel prize winner, recently appointed to the chair of biochemis- 
try at Oxford University. This has been one of the greatest recent 
triumphs in biochemistry. In simple terms it can be described as 
follows and summarized as in Fig. 4. The mechanism is somewhat 
involved but can be followed if Fig. 4 is carefully studied. 

, CITRATE 

Ace.,1 - - ' V CTbondioxid, 

coenzyme A 
20 

/ \ 

OXALOACETATE SUCCINATE ^ Carbon dioxidt 



Citric acid cycle 

Fig. 4 The citric acid cycle. 

Each molecule of acetyl-coenzyme A, with its two carbon atoms, 
unites with a molecule of a 4-carbon compound, oxaloacetic acid. 
The product, citric acid, with six carbon atoms, is then degraded 
step by step by a complex system of enzymes and coenzymes, loses 



214 What Is Science? 

first one and then a second carbon atom, each in the form of car- 
bon dioxide, and leaves a residual 4-carbon substance, namely suc- 
cinic acid. Further enzymic manipulations of the latter lead back 
through a series of successive reactions to the regeneration of oxalo- 
acetate, with which the cycle began and which can then take up a 
further molecule of acetyl-coenzyme A. In this way a very small 
quantity of oxaloacetate can be used over and over again and can 
participate in the breakdown of relatively large quantities of acetyl- 
coenzyme A. Each pair of carbon atoms entering this cyclic system 
in the form of acetyl-coenzyme A, no matter what its origin, emerges 
in the form of carbon dioxide, the common end product of oxidation 
of fat, carbohydrate and protein alike. This important mechanism is 
known as the citric-acid cycle. 



Energy Metabolism 

The foregoing pages have presented an outline of some of the main 
features of the "how" of katabolism and, indeed, investigations of 
the "how" were in progress for many years before there was anything 
more than the most superficial of answers to the question of "why/' 
Why, in fact, do living organisms make use of the complicated and 
often lengthy, step-by-step mechanisms they do when the same even- 
tual results could be obtained by simply throwing the materials on 
the fire? If, ten or fifteen years ago, one asked a biochemist why 
living organisms oxidized this substance or that to carbon dioxide, 
the chances are that he would have replied "to get energy, of course." 
But that "of course" only served to conceal a massive ignorance of 
the mechanisms whereby chemical energy tied up in the food mole- 
cules is made accessible to the organism and how, having been made 
accessible, this energy is harnessed and transformed into mechanical 
work, as it is in muscle; or into electricity, as it is in the peculiar 
electric organs of certain fishes; or into light, as it is in fireflies; or 
into any other of the large number of energy-expending activities 
that are invariably associated with the business of living. To these 
problems we are beginning to find some answers, though much still 
remains to be done. 



Biochemistry 215 

Mostly these problems center around a somewhat complex com- 
pound, adenosinetriphosphate, known familiarly though by no means 
contemptuously as ATP. Muscular contraction, electric discharge, 
light production and a whole host of synthetic biochemical reactions 
and processes are known to be more or less immediately associated 
with the breakdown of ATP into ADP (adenosinediphosphate), and 




Energy ^ 



y Mechanical work 

Electricity 
-Alight 

v Chemical synthesis 
^Heat 



Fig. 5 The energy cycle. The ATP/ ADP cycle resembles a dynamo, 

driven by a motor in the form of katabolic reactions. Energy generated by 

the dynamo is drawn off and passed through the appropriate biological 

transforming devices to do mechanical, electrical or other worfe. 

this breakdown, in its turn, is known to be associated with the re- 
lease of large amounts of energy. Each molecule of ATP thus broken 
down yields a perfectly definite unit packet of energy which might 
be called a "biochemical quantum." Now if this energy is set free 
by a simple, straightforward chemical method such as acid hydrolysis, 
it appears in the form of heat. If the breakdown takes place in a 
muscle, however, the energy appears for the most part in the torn* 
of mechanical work. Evidently the muscle contains some system that 
can act as a transformer of chemical into mechanical energy. As yet 
the precise nature of this "transformer" is not fully understood, but 
at any rate it can be stated that the contractile portions of the 
muscle act as an enzyme that specifically catalyzes the breakdown 
of ATP into ADP and, moreover, that they shorten as they do so. 
If then the breakdown of ATP is at the back of energy-consuming 
processes as a whole and there is every reason to think that it is 
it follows that, since the amounts of ATP present in living tissues 
are comparatively minute, fresh supplies of this substance must be 



216 What Is Science? 

constantly forthcoming from somewhere or other. And, in fact, the 
formation of ATP seems to be practically the sole aim and object of 
katabolism as a whole. An example of one such sequence of reactions 
is shown in Fig. 6. 




To oxidative machinery - 



COOH 

tenol-pyruvic 
acid) 



Fig. 6 Formation of ATP in the course of carbohydrate metabolism. 

The "energy-rich" phosphate is written as ~ instead of the more usual 

(?) which represents an "ordinary" or "energy-poor" phosphate. 

The katabolic breakdown of, say, glucose is a step-wise process and 
at each step a new compound is formed from its immediate pred- 
ecessor in the procession. At certain of these steps phosphate is taken 
up from the surroundings and incorporated into the new molecule, 
which then undergoes some perfectly definite and as a rule com- 
paratively simple, enzyme-catalyzed reaction such as oxidation or 
dehydration. As a result, about the theoretical basis of which we 
know very little indeed and which therefore cannot be very clearly 
described, a portion of the chemical energy of the new product 
becomes intimately associated with the phosphate radicle, converting 
what was formerly an "energy-poor" phosphate radicle into one that 
is "energy-rich." Next there ensues a reaction between this energy- 
rich product and ADP in which the phosphate radicle, together with 
the energy with which it is associated, is transferred to the ADP so 
that a new molecule of ATP is synthesized and available for whatever 
effector activity is required of the tissue. Here again we come upon 
a process that is essentially cyclical in character, ATP and ADP 



Biochemistry 217 

undergoing a constant interchange, energy from katabolic reactions 
being used on the synthetic side of the cycle and transformed into 
one or another kind of biological work on the other. 

Most important among the energy-yielding reactions of katabo- 
lism are those which collectively make up the citric-acid cycle, partic- 
ularly those which bring about the oxidation of certain of the in- 
termediates. For example, the oxidation of each molecule of the 
4-carbon compound, succinate, is attended by the synthesis of two 
molecules of ATP from ADP. Smaller yields arise from processes such 
as glycolysis, and one ATP molecule is probably formed each time a 
2-carbon unit is detached from a fatty acid. All in all, so efficient 
is the energy-capturing machinery of the body that, of the chemical 
energy which enters the animal body in the form of food, some- 
where between two-thirds and three-quarters can be "trapped" in 
the form of ATP. 

Obviously enough, food in the form of fats, proteins and carbohy- 
drates must be provided to an animal in amounts large enough to 
furnish the energy it expends in the course of its everyday life. It 
will lose weight on less and get fat on more. Furthermore, if we 
know the energy expenditure of a given individual, animal or human, 
it is possible to calculate its minimum requirements in the matter of 
food. Elaborate experiments have been made in which animals and 
humans have been kept in confined quarters surrounded by ap- 
paratus which enables their total heat production to be measured 
with a very high degree of accuracy, Many such determinations have 
been carried out and the energy output of men lying at rest, men 
riding stationary bicycles, sawing wood, reading and doing other kinds 
of work are accurately known. The energy yields of many different 
kinds of food, measured again as heat, have also been determined, 
and when the amount of energy dissipated as heat by an individual 
doing work of some kind is compared with the amount of heat 
which would be generated by the combustion of the amount of 
material metabolized in the course of the experiment, the figures 
agree very closely indeed. Data of this kind form the basis of the 
calculations of calorie requirements which were so much in evidence 
a few years ago. 



218 What Is Science? 

Vitamins 

Whereas green plants, and together with them a few groups of bacte- 
ria, can synthesize everything their life requires from water, salts, 
carbon dioxide and some simple nitrogenous compound such as 
nitrate, organisms of other kinds are unable to achieve this. Animals 
in particular are synthetically deficient in the sense that they are un- 
able to produce many of the substances required for the maintenance 
of their substance or machinery. These must be obtained from the 
food. For example, we have seen that animals cannot produce all 
the amino acids they require; for the so-called essential amino acids 
they must rely on their food. In the end this means that they rely 
upon the green plants, directly if they are herbivorous, indirectly at 
second- or third-hand if they are carnivorous. These essential amino 
acids are needed largely for the maintenance of body structure and 
for the synthesis of enzymes and a number of hormones, but over 
and above the essential amino acids there is a long list of nutritional 
requirements for which again animals have to rely upon their food 
and again, in the long run, on green plants. These substances are 
the vitamins. 

The daily requirement for most vitamins is of the order of milli- 
grams or fractions of a milligram per kilogram of body weight per 
day, but deprivation of any one of these substances leads to one 
or other kind of deficiency disease. That certain diseases can be cured 
by suitable modifications of the diet has, of course, been known for 
many centuries at least. For example, Hippocrates knew that night 
blindness, an early sign of vitamin A deficiency, can be cured by 
eating liver, a tissue that is relatively rich in that particular vitamin. 
Hippocrates' knowledge has an echo still today, for it is usual to 
provide the pilots of night-flying airplanes with ample supplies of 
vitamin A. Another long-familiar deficiency disease is scurvy, which 
is preventable and curable by vitamin C (ascorbic acid). Interestingly 
enough the early signs of vitamin C deficiency include extreme ir- 
ritability and bad temper, and it will be recalled by readers of sea 
stories that outbreaks of scurvy on board ship were frequently pre- 
ceded by mutinous tendencies among the crews. Captain Cook pro- 



Biochemistry 219 

tected his crews against scurvy and, incidentally, earned for them 
the sobriquet of "limeys" by insisting on the provision and consump- 
tion of lime juice on his ships, the lime, in common with other 
citrus fruits, being as we now know a rich source of vitamin C. 

It seems strange today that the establishment of the vitamin con- 
cept was delayed until the early years of this century. The notion 
that diet can influence disease was dismissed as nothing more than 
an old wives' tale by many (and the medical profession was no ex- 
ception) who should have known better. The final conviction that 
had hitherto been lacking came mainly from certain experiments of 
the late Gowland Hopkins, for fifty years professor of biochemistry 
at Cambridge and one of the pioneers perhaps the greatest of bio- 
chemistry as an independent science. Young rats were chosen as 
subjects; young because, as they were still rapidly growing, their 
nutritional requirements would be large and they would be all the 
more likely to show the effects of any dietary deficiency to which 
they might be subjected. All the animals received a diet, ade- 
quate in amount, but made up from carefully purified fat, protein 
and carbohydrate, together with water and salts. One half of the 
animals received in addition a few drops of milk daily while the 
other half did not. The group without milk grew less rapidly than 
normal and later stopped gaining weight altogether and became 
exceedingly ill. The group receiving milk grew well and at a normal 
rate. Then, with a stroke of the genius so typical of Hopkins, the 
diets were switched over. The animals that formerly grew well stopped 
putting on weight after a few days and fell sick, while the remainder 
rapidly improved in health and began again to grow. This beautiful 
experiment demonstrated as conclusively as could be wished that 
there exists in milk some substance or substances of which extremely 
small quantities are required for normal growth and for the main- 
tenance of the health and vigor of animals kept on a purified diet 
that was adequate in every other respect. Few remained unconvinced 
thereafter. 

This experiment is representative of one of the two main proce- 
dures used in carrying out experiments on the nutritional require- 
ments not only of animals but also of microorganisms such as bacte- 
ria. Starting with a diet or culture medium known to be inadequate 



220 What Is Science? 

to support the normal life of the experimental subjects, various likely 
substances can be added until the diet or medium becomes adequate. 
Alternatively one can start with a diet that is known to be adequate 
and remove one constituent after another until it becomes inade- 
quate. The latter method has been used in many animal experiments 
and comparable experiments have been carried out on bacteria. Many 
bacteria can only be cultured in the laboratory on complex media. 
Many milk-souring organisms, for example, normally live in milk 
but can be cultured on suitable synthetic media, always provided 
that they are supplied with riboflavin. This substance is present in 
milk and if it is removed the bacteria are no longer able to multiply. 
It might be thought that if a cheap method could be discovered 
for removing this substance from raw milk the often troublesome 
phenomenon of souring could be avoided, but if this were done it 
would be undesirable in another way, for riboflavin is a vitamin for 
animals as well as for these particular bacteria. 

Other experiments on other kinds of bacteria have brought to light 
the existence of a large number of bacterial vitamins or "growth 
factors." Not all bacteria have the same nutritional requirements 
and in this respect they differ markedly from animals, all of which, 
large or small, vertebrate or invertebrate, have substantially the same 
vitamin and other nutritional requirements. It is however noteworthy 
that the bacterial vitamins, where necessary, are usually identical 
with vitamins required by animals, suggesting that different though 
these minute, unicellular organisms are in every way from animals, 
their metabolism must probably be organized on a similar general 
plan. 

Organisms that require this or that vitamin are said to be "exact- 
ing" for the particular substance concerned, and although animals 
as a whole are very exacting, some bacteria, notably some of those 
responsible for certain kinds of blood poisoning, are even more exact- 
ing than are the animals. Some of them require to be provided with 
about twenty amino acids and half-a-dozen or more vitamins, all of 
which are normally present in animal tissues. Bacteria with such 
extensive nutritional requirements as these are likely to find every- 
thing they need only in the tissues or tissue exudates of a living 
animal and so are commonly parasitic and, as a general rule, are 



Biochemistry 221 

highly pathogenic at the same time since they frequently produce 
powerful toxins. Some of these bacterial toxins have now been iso- 
lated and found to be enzymic in nature. One of those produced by 
the gas gangrene organisms, for example, is an enzyme that digests 
and liquefies the tissues in the vicinity of the infected area, thus 
providing a rich medium for the growth of the bacteria and allowing 
them to spread rapidly and extensively through the tissues; but this 
is by the way. Before leaving the bacteria and their nutritional re- 
quirements, however, mention may be made of a bacterial vitamin 
that is required by most streptococci, namely />-aminobenzoic acid, 
and to this we shall refer again presently. 



The Functions of Vitamins 

A good deal is known today not only about the multiplicity and 
chemical identity of the vitamins but also about their functions. For 
instance, vitamin A is now known to yield by oxidation a derivative 
which, in combination with the appropriate protein, forms visual 
purple, a retinal pigment that is particularly concerned with vision 
in dim light. Again, vitamin D is required to facilitate the absorption 
of dietary calcium, though how it does so is not known. In its 
absence bones are not properly or even sufficiently calcified, so that 
they bend under the weight of the body, leading to rickets in the 
child, and, after prolonged deprivation in adults, to the hideous 
deformities of osteomalacia. On the larger scale, the provision of 
vitamins A and D in the form of cod-liver oil and of C in the 
form of orange juice to every child in the United Kingdom during 
the years of the Second World War virtually banished rickets from 
the country, reduced the incidence of dental caries and produced 
what is probably the finest and best developed generation of children 
to be found outside Utopia. And this in spite of the rationing of 
fats, proteins and carbohydrates. 

From the more biochemical point of view, most interest attaches 
to the B group of vitamins. Here the old alphabetical system of 
nomenclature has been virtually abandoned and the numerous sub- 
stances covered by the old title of "B complex" are now known by 



222 What Is Science? 

their chemical trivial names. Some at least of the functions of 
most of them are already known. Thus thiamine (Bi) forms part of 
a coenzyme that plays a major role in the conversion of pyruvate to 
acetyl-coenzyme A (Fig. 3). Coenzyme A itself is a derivative of 
pantothenic acid, another of the B vitamins. Nicotinic amide and 
riboflavin form parts of the cocnzymes or prosthetic groups of numer- 
ous oxidizing enzymes, several of which, like acetyl-coenzyme A, are 
intimately bound up with the operation of the citric-acid cycle (Fig. 
4). Pyridoxal again forms part of the prosthetic group of the 
transaminases, the enzymes which catalyze the deamination of the 
amino acids. 

Small wonder then that any deficiency of any one of the B vitamins 
leads to more or less serious derangement of normal metabolism and 
to the disorganization of the innumerable natural processes that de- 
pend upon and are indissolubly linked with it. Probably there remain 
yet other functions of these vitamins still to be discovered. It is even 
conceivable, though perhaps not very probable, that there are other 
vitamins as yet undiscovered, but in the meantime there are few 
fields of human endeavor that have already done more, and can do 
more still, to promote the health and efficiency of the whole human 
species, no matter what its race, its color or its creed. 



Hormones, Antibiotics and Bacteriostatics 

Among its other interesting and important achievements are those 
which biochemistry has contributed to pharmacology and therapeu- 
tics. The discovery of hormones, primarily an achievement of phys- 
iology, provided the raw materials for a vast amount of biochemical 
research which led to the eventual isolation, identification and, in 
some cases, the synthesis of these important bodies. Some of these 
substances are comparatively simple, others exceedingly complex. Ad- 
renalin and thyroxin are two of the simpler ones; both are derived 
from the amino-acid tyrosine. Insulin on the other hand is very com- 
plex, being a protein, though a comparatively simple substance as pro- 
teins go. Mention has already been made in this essay of the use of 



Biochemistry 223 

insulin in the control of diabetes and this is but one of many cases 
in which hormones are employed in the service of medicine. Other 
examples include the use of thyroxin in the treatment of goiter and 
the use of the sex hormones in the management of sterility, habitual 
abortion and menopause. Among the more recent discoveries are the 
cortical hormones including cortisone, for the value of which in the 
treatment of arthritic conditions so many claims, many of them un- 
fortunately extravagant, have been made. Side by side with these 
discoveries have been those of synthetic estrogens such as stilbestrol, 
compounds which produce the same physiological effects as the nat- 
ural female sex hormones and which have not only the advantage 
of cheapness as compared with the natural products but are perhaps 
less likely to be carcinogenic. They are used, in fact, for the control 
of carcinoma of the prostrate gland in males, one of the few forms 
of cancer that can be checked almost indefinitely without surgical 
intervention. 

These are cases in which the biochemist has taken over and 
enormously developed fundamental discoveries made in related fields 
of biological science. At least one noteworthy triumph similarly 
achieved lies in the field of antibiotics. Fleming's discovery of penicil- 
lin, originally an accident, came out of bacteriology, but it was only 
when biochemists came into the field that this important substance 
was concentrated, purified and eventually marketed in the pure form, 
for the isolation of the small quantities of penicillin produced by 
large-scale cultures of the mold, Penicillium, requires techniques of 
the kind developed by biochemists for the isolation of so many other 
important biological substances. Similar techniques were also used 
for the later isolation of many other new and potent antibiotics such 
as streptomycin, terramycin, aureomycin, chloromycetin and the like. 

Biochemistry has also contributed much to developments in our 
knowledge of synthetic bactericides and bacteriostatics. The com- 
bined efforts of organic chemists, pharmacologists and clinicians 
have been concerned since the days of Ehrlich with attempts to 
produce synthetic chemicals which, while relatively innocuous to hu- 
man patients, would yet kill off or check the growth of pathogenic 
microorganisms. In the case of streptococci in particular, the introduc- 



224 What Is Science? 

tion of sulfanilamide and its present-day legion of derivatives has 
made it possible to cure many diseases of streptococcal origin, many 
of which formerly were frequently fatal, e.g., pneumonia, blood 
poisoning of various kinds, gonorrhea and so on. Sulfanilamide is 
not a bactericide but a bacteriostatic; it does not kill the responsible 
organisms but does check their further multiplication, leaving the 
natural leucocytic defenses of the body to pick off the invaders. 
Biochemists asked why, and it was the application of knowledge and 
concepts gained by the study of what is known as the "competitive 
inhibition" of enzymes that provided an explanation for the mode 
of action of the sulfonamides. 

The reason appears to be that sulfonamidc-sensitive organisms 
require p-aminobenzoic acid as a growth factor or vitamin. Little is 
known about the part this substance plays in the metabolism of 
bacteria but it is certain that in its absence they fail to grow and 
may even die. Presumably therefore p-aminobenzoic acid forms an 
important part of the metabolic machinery of the cells. However, 
certain other substances which resemble />aminobenzoic acid in struc- 
ture but are unable to discharge its functions, can also gain access 
to the site at which -aminobenzoic normally acts. If such a sub- 
stance and ^-aminobenzoic acid are both present, they compete for 
possession of the site and on the outcome of this competition the 
fate of the cell depends. Sulfanilamide is such a substance. Provided 
that it can be applied at sufficiently high concentrations, as is possi- 
ble because of its relatively low toxicity, it is able to compete with 
and exclude the essential p-aminobenzoic acid and can thus put an 
end to the growth and multiplication of the microorganisms. This 
notion of "competition" between a natural vitamin and an artificial 
structural analogue is an exact parallel of the phenomenon known to 
biochemists for many years as competitive inhibition. 

The same notion has been widely extended. Already a large group 
of "vitamin antagonists" or "anti-vitamins" have been synthesized 
and their action tested on various bacteria. Unfortunately, few of 
these have proved sufficiently nontoxic for therapeutic use, though 
many have proved to have powerful bacteriostatic or even bactericidal 
properties, and this remains a very active and very promising field 
of biochemical research. 



Biochemistry 225 



Conclusion 



Such then are some of the facts that have been established by the 
application of chemical methods and concepts to living subjects; in 
short, by biochemistry. Every kind of living material animals, plants 
and microorganisms of every kind is a legitimate object for bio- 
chemical study. Indeed, biochemistry is perhaps more a way of think- 
ing, a way of attacking biological problems, than a mere "subject." 
There is room for biochemistry and yet more biochemistry in every 
branch of biological science, in clinical medicine and in veterinary 
practice today, and, on the academic side, perhaps it is to biochemis- 
try that we may look for a reunification of all the biologies into 
the one vast and universal Biology which time and inevitable de- 
partmentalism have so industriously dismembered in the past. 



BIOLOGY 



WARDER CLYDE ALLEE 



about 

Warder Clyde Allee 



Dr. Allee died in Gainesville, Florida, on March 18, 1955, shortly be- 
fore his seventieth birthday, after writing this contribution. He was 
one of the country's leading students of animal ecology and behavior. 
He will be remembered no less for his integrity, his elevated outlook 
on human relationships and his courage in adversity than for his dis- 
tinguished professional achievements. 

When I originally asked Dr. Allee to send me a few biographical 
notes about himself he sent me the following graceful account. I give 
it exactly as he sent it. 

"I was born and grew up on a small farm in West Central Indiana 
not far from the Wabash River. My mother, who was 98 in De- 
cember 1954, was born and is still living on the same farm, a part of 
which her maternal grandfather had bought from the government 
when he emigrated from North Carolina in the early 1800s. We 
lived on the outer fringe of a sizable Quaker settlement. I was grad- 
uated from the Friends Academy the day after my seventeenth birth- 
day and began teaching that fall in a one-room country school called 
Frog Pond. 

"I taught grade school for three years, was graduated from Earl- 
ham College in 1908, taught high-school biology during my senior 
year and for two years more, and received my Ph.D. in zoology summa 
cum laude at the University of Chicago in 1912. Summers spent in 
research and teaching at the Marine Biological Laboratory in Woods 

228 



about Warder Clyde Allee 229 

Hole, Massachusetts, on Cape Cod, furnished my most important 
professional experience for the following nine years much more im- 
portant than the winters of those years, during which I held successive 
teaching posts at the University of Illinois (where I taught botany), 
Williams College in Massachusetts, University of Oklahoma and 
Lake Forest College in Illinois. 

"Then followed 29 years of teaching zoology at the University of 
Chicago, with research there and at Woods Hole, and with interest- 
ing and somewhat lengthy study trips to Panama, California, and 
Utah. 

"Age 65 brought compulsory retirement at Chicago and immediate 
appointment as head professor of biology at the rapidly developing 
University of Florida. 

"Conspicuous activities have included the initiation of the found- 
ing of Ecological Monographs and Physiological Zoology, the latter 
by the University of Chicago Press. I have been on the editorial board 
of Physiological Zoology from the start and managing editor since 
1930. 1 was invited to Paris, France, in 1950 with all expenses paid to 
take part in a colloquium. 

"My long years of work with the Chicago Regional Committee of 
the American Friends Service Committee early brought me into close 
working contact with Miss Jane Addams of Hull House, with Rufus 
Jones and Clarence E. Pickitt of Philadelphia, and with many more, 
particularly with people from distressed countries in many parts of the 
world. 

"I mention with hesitation, since I need no sympathy, that after 
an extremely active youth and young manhood, for years I have been 
a paraplegic confined to a wheel chair." 

Dr. Allee was married in 1912 to Marjorie Hill, and had two grown 
daughters. His first wife died in 1945 and eight years later he married 
Ann Silver. Besides the places mentioned in his account, he taught 
at Utah Agricultural College and the University of California, and 
was Harris Foundation lecturer at Northwestern University (1938] 
and Prather lecturer at Harvard (1953). He was a. member, among 
others, of the National Academy of Sciences, the American Academy 
of Arts and Sciences, the Philadelphia Academy of Science, the 
British Ecological Society, the Florida and Illinois Academies oj 



230 What Is Science? 

Science. He wrote more than 150 journal articles and his books, to 
mention only a few, are Jungle Island (with M. H. Allee, 1925); Ani- 
mal Aggregation, a study in general sociology (1931); Animal Life and 
Social Growth (1932); Ecological Animal Geography (with R. Hesse 
<ind K. P. Schmidt, 1937 and 1951); The Social Life of Animals 
(1938); Principles of Animal Ecology (with A. E. Emerson, O. Park, 
T. Park and K. P. Schmidt, 1949). One of his best known books, Co- 
operation Among Animals, with Human Implications (1951), deals 
with a theme close to his heart and considered in the following essay. 



BIOLOGY 

WARDER CLYDE ALLEE 



How did life originate? This most serious and searching question in 
all biology is usually avoided, especially in short essays. We actually 
know so little about how life began that much time is required for 
repeating and repeating our own uncertainties. This was not always 
true. I knew in my boyhood on a back-country Indiana farm that life 
had been created by a kindly, very wise, so-capable "Mr. Jehovah," 
and that was that. It is a far cry from a religion leading to that point of 
view to the one outlined later in the present chapter. 

Many, not at all content with such a solution of the problem, are 
still puzzling away at the proper answer, which, I repeat, remains un- 
known. One of the better guesses is that when the earth was much 
younger its atmosphere contained no oxygen and the upper layer of 
ozone had not developed. Under those conditions all the ultraviolet 
rays of the sun reached the surface of the earth, including those of 
the short ultraviolet region of the sun's spectrum. Given a favorable 
temperature, moisture, and the needed concentration of inorganic 
chemicals, these energy-rich ultraviolet rays could supply the driving 
power needed for the formation of molecules closer to being alive 
than were any others then in existence. 

This suggestion has received considerable, though not conclusive 
support, from a simple experiment reported in 1952 by Stanley Mil- 
ler, then a graduate student in chemistry at the University of Chicago. 
Miller arranged a simple set of glass tubing and a flask in which he 

231 



232 What Is Science? 

placed water, partly as vapor, and three gases such as were present in 
the early atmosphere of the earth. He then tightly sealed all openings. 
In addition to water vapor the gases were hydrogen, ammonia, and 
methane, which is the scientific name for marsh gas. These were made 
to circulate past a weak corona light produced by a constant electric 
discharge. Such a discharge was probably present when the earth was 
young. It was rich in ultraviolet rays as well as in other kinds of energy. 

At the end of only a week's time, the water contained amino acids 
although none were present at the start, and none had been intro- 
duced. Amino acids are the ''building stones" of proteins, and protein 
is basic for living protoplasm. This experiment did not produce life 
from nonliving matter. It does lend strong support to the idea that 
the organic compounds that serve as the basis of life were formed in 
some such fashion. 

The exact nature of the first somewhat lifelike molecule, just like 
the processes by which it came into being, is unknown. It might have 
contained phosphorus, and the energy required for making a simple 
protein-like linkage could have been supplied from a single phosphate 
bond. All this synthesis would have taken place before the develop- 
ment of green chlorophyll, which is able to form the sugars and 
starches required by most present-day plants and animals. 

All living organisms probably evolved from some such beginning, 
and all biology, in its diverse phases, traces back to these scarcely liv- 
ing particles. Some excellent students of the subject use biology as 
the covering name for the consideration of more general principles 
that involve both plants and animals. Material dealing mainly with 
plants is delegated to botany; that concerning animals to zoology. 
These in turn are broken up into smaller specialities such as proto- 
zoology, entomology, and mammalogy, which are still further sub- 
divided. 

A second standard division of biology is based on the type of 
study being made rather than on the kind of organism. As a result 
the discussion is broken into such categories as morphology, which 
treats of form and structure; physiology, which deals with functions of 
living things, or of their parts; ecology, which concerns relations be- 
tween organisms and their complete environment; cytology, the study 



Biology 233 

of cells; genetics and evolution, which have a chapter devoted to them 
in the present book, and many more including biogeography. Re- 
spectable, and even lively, books are available on each of these sub- 
divisions. 

Excellent summarizing essays on biology have been written using 
these topics as a working outline, witness for example the compre- 
hensive survey in recent printings of the Encyclopaedia Britannica. 
This approach has not been used here primarily because of my feeling 
that it is too didactic for a book of this kind, that it would hurry the 
reader along and burden him with too many facts. Then, too, al- 
though I have great respect for the bodies of knowledge in each of 
these fields, and, year after year, I continue to be much interested by 
the research discoveries in many of them, much of the accumulated 
information, even in my own special field of ecology, frankly bores 
me. 

I have adopted, therefore, a much less formal and systematic pre- 
sentation, which concentrates on the material that catches and holds 
my mature, critical interest somewhat as it did in my youth. 

I propose to say nothing about the difficult problems of classifica- 
tion (it is relatively easy to tell a cow from a tree but no expert really 
knows how to draw the line between one-celled plants and the sim- 
plest protozoan animals). However I shall discuss a more important 
area of uncertainty, the border zone between living and lifeless mat- 
ter that has never been alive. The principles of ecology will be dealt 
with. Some of my experiences in a tropical rain-forest in Panama 
will help to illustrate them. In examining the behavior response of 
animals to their surroundings, I intend to consider the contributions 
of learning and adaptation, as well as inherited instinct, to complex 
behavior patterns. This leads to a subject which has long preoccu- 
pied my thoughts, the subsocial and social life of ncnhuman animals, 
and of man. Three aspects of sociality require attention: the simple 
types of organization, the widespread tendencies toward the begin- 
ning of co-operation, the relative biological importance of proto- 
co-operative, and their opposite, disoperative effects. Finally, I should 
like to take up the relation between biology and religion, that is, a 
scientifically oriented religion which accords with my own interpreta- 



234 What Is Science? 

tions and conviction. It is the unity rather than the traditional con- 
flict between biology and religion (a unity supported by recent bio- 
logical findings) that I intend to examine. 

This is the discursive and somewhat personal path I mean to follow; 
perhaps in this way I can succeed in communicating some of the ex- 
citement of biology that continues to grip me after fifty years of study. 
I return now to the main thread of the discussion. 

A thought-teasing suggestion is that an early kind of life was virus- 
like. At least we know that living, growing virus can form into appar- 
ently lifeless crystals, which start to grow again when placed in suit- 
able surroundings. Thus apparently lifeless crystals of the virus causing 
tobacco-mosaic disease will grow if placed on a live tobacco leaf under 
proper conditions. However, there is always the objection that mod- 
ern viruses live only as parasites, which appears to mean that they have 
undergone a long evolutionary degeneration. Perhaps their parasitic 
habit shows, however, that they are really so simple, as were their 
ancestors before them, that living as parasites is the only way they can 
survive in the modern complex world. 

If life did originate somewhat as I have sketchily suggested, there is 
at least one potent reason why it is not continuing to be formed so 
today. Now, the suitable niches are all occupied by efficient living 
forms such as bacteria that would kill off newly formed, simple, living 
molecules by feeding on them. 

Other possible relations of the viruses are suggestive. It is a well- 
known laboratory process in modern organic chemistry to shift the 
location of ions within the molecule. Indeed, a given kind of ion, 
hydrogen for example, may be replaced, say by sodium, in routine 
laboratory work, thereby changing the properties of the whole com- 
pound. 

The viruses that are capable of being crystallized are tempting ob- 
jects on which to try similar chemical techniques in the hope that 
the altered virus may present highly significant changes in its basic 
properties. Perhaps such man-produced shifts in the arrangement of 
ions may, for example, change a virulent disease-causing virus into a 
related form that is entirely harmless to the same host, and so cause 
virus evolution to take place. 

These simplified, condensed suggestions regarding the origin of life 



Biology 235 

and the chemistry of virus bring us to a conclusion of great and basic 
importance. Living matter, for all its complexities, consists of the same 
sorts of substances that compose the nonliving world. No new, special 
chemicals are required, and many of the basic techniques and proce- 
dures developed for different phases of chemistry can be applied suc- 
cessfully to the study of living structures and processes. 

It is a long jump from particles that are barely living, if that, to 
the complexities of modern plant and animal life. Even the simplest 
one-celled plants, known as algae, and their counterparts among ani- 
mals, the protozoans, are remarkably complicated physical-chemical 
systems. Hints toward bridging the gap between particles that seem 
to have only the beginnings of being alive and the most generalized 
plants or animals will not be discussed here. However, the somewhat 
similar problems raised in trying to cross the large gaps between dif- 
ferent kinds of living things are dealt with in Julian Huxley's discus- 
sion of evolution, and in references cited by him. 

Life, the central theme of this chapter, is hard to define. But living 
beings do have some common characteristics, the listing of which al- 
most makes a definition of life. These are: 

1. All can change other matter into protoplasm thus assuring the 
maintenance, growth, and repair of their bodies. All living things 
also destroy material, even of a part of their own protoplasm, and 
make use of some of the energy that is released. 

2. All grow by complex internal processes. 

3. All reproduce their kind. 

4. All continuously adjust to their environment. 

5. All show at least a foreshadowing of co-operation. 

No one of these characteristics will separate the living from the life- 
less. At least partial transitions occur for each one, yet the total of all 
five does become a relative, if not an absolute definition of life. Liv- 
ing beings are not sharply and distinctly set off from lifeless matter, 
and the physics and chemistry of living protoplasm, although more 
complex, are not really different from similar relations of nonliving 
stuff. This conclusion accords with modern ideas of how life origi- 
nated. Although complete identitv is not yet finally demonstrated, the 



236 What Is Science? 

assumption of similarity between lifeless and living matter forms the 
fertile working hypothesis of present-day biology. 

The relation between plants and animals and their whole environ- 
ment, including one another, forms the currently almost popular and 
very important field of ecology. Some of the underlying principles of 
ecology are summarized briefly in the following paragraphs. The sim- 
plest principles deal with the physical surroundings rather than with 
plants and animals. A pigpen is more easily described than the pigs 
living in it, though pigs are much more interesting and important 
than their pen. 

Living processes are normally impossible in a vacuum. To be sure 
crystallized virus, or spores, seeds, and small forms, if surrounded by 
coverings that cannot readily be penetrated, survive prolonged ex- 
posure in a vacuum. But active living beings require an environment 
with which they can establish close working relations. 

Living forms are under the influence of their surroundings, and, in 
turn, they influence them. Thus there is good evidence that the oxy- 
gen, which forms a fifth of the air today, was first produced, as it is 
still formed, by green plants as a by-product of the photosynthesis 
that makes sugars and starches. 

Needed elements of the environment must be present above some 
minimal amount to be of use to a given plant or animal. This is known 
as the principle of the minimum. For example, although oxygen forms 
approximately twenty per cent of the atmosphere, it is only slightly 
soluble in water where, under good conditions, only about a half of 
one per cent of dissolved oxygen is available for respiration; often 
even less is present. As the dissolved oxygen content of the water falls 
lower and lower, it becomes more and more of a limiting factor. 
The principle of the maximum applies to the opposite condition in 
which richness rather than scarcity becomes the limiting condition. 
Too much rather than too little is present. Such a condition is shown 
with heat, but normally does not occur in relation to oxygen, except 
for the so-called anaerobic bacteria and a few other organisms that 
are oxygen intolerant. The associate principle of the optimum, when 
neither too little nor too much is present, can easily be made appar- 
ent. In a complex environment containing many important aspects, 
the ecological optimum may not be the best condition for the par- 



Biology 237 

ticular plant or animal so far as any one factor is concerned, and yet 
be the optimum for the whole community. 

One of the most exciting principles of ecology deals with the re- 
markable fitness of the environment for life as we know it. In theory 
it is possible for a form of living stuff to have evolved on the cold 
outer planets, where the temperature is much, much lower than it is 
on the earth. There, ammonia might be the key compound, as water 
is with us. Ammonia has a considerably lower freezing point than 
water. It is markedly less fit as a basis for life since, among other con- 
siderations, it forms firm chemical compounds much more readily 
than does water. 

Life could also exist at a much higher temperature than character- 
izes the earth's climate. A living system is possible at too high a tem- 
perature for carbon to be the common, basic organic element as it 
is with us. Silicon might be substituted under such conditions, al- 
though silicon is less fit than is carbon to form the basis for the com- 
plex physiology of life. 

I still find it literally astounding, as a group of us put it a few years 
ago in a so-respectable and so-scientific book called Principles of Ani- 
mal Ecology, that the surface of a solid body such as the earth 
placed as it is, neither too close to nor too far from an energy-giving 
sun docs actually provide an excellent general environment for the 
living organism. It was possible for the late biochemist Lawrence Hen- 
derson of Harvard to maintain that this is basically "the best of all 
possible environments for life." This conclusion, published in 1913, 
has not been successfully contradicted to date, although, obviously, 
not all of earth's habitats, deserts, for example, are ideally fit places 
for life in general. Apparently, believe it or not, we live in what ap- 
proaches being fundamentally, the best of all possible physical 
worlds. 

There are ever so many more ecological principles, far too many for 
consideration here though each is significant, and the matters sum- 
marized can be interesting, too. Discussion of one more will suffice at 
this point. A whole set of principles centers upon light, and one of the 
most striking of these states that many reactions to light by both 
plants and animals are stimulated to occur when the intensity of light 
multiplied by the length of exposure reaches a constant value at or 



238 What Is Science? 

above the threshold of stimulation. The working of this principle is 
well illustrated in photography. Beyond the upset value for the pho- 
tographic film, the more intense light calls for shorter exposure to 
produce a given effect. Oat seedlings, which turn toward the light 
equally if exposed to 0.00017 candle-meters (one candle power of 
light at a meter's distance is one candle-meter) for 23 hours, 18 min- 
utes, will give the same strength of reaction if stimulated by 26,520 
candle-meters for 1/1000 of a second. In each instance the product of 
the two values is approximately the same in candle-meter seconds, 
26.3 to be compared with 26.5. Similarly, the horseshoe crab, Lim- 
ulus, of the Atlantic coast south of Maine, in the presence of a con- 
centrated source of light in a dark room, turns and moves away from 
it. When exposed to light from two sources that differ in intensity, it 
will turn and move away in a direction determined by the angles at 
which the two beams reach the eyes together with the product of in- 
tensity and duration of exposure to the lights. 

In one of the first experimental series with the horseshoe crab, out 
of 48 individuals tested, all but ten reacted in fairly diagrammatic 
fashion; these ten gave unpredictable results. This introduces another 
principle. It is remarkable and significant that although 38 of these 
highly complex animals behaved in their reaction to light as though 
they were slow-moving guided missiles, the other ten reacted in an 
unpredictable manner. As we used to say at the University of Chicago, 
the reaction of those ten illustrated what we called the Harvard law 
of animal behavior, which holds that under controlled conditions 
animals do as they damn please. The facts are real; the name is a teas- 
ing joke. 

Ecology, and other parts of biology are like that. Life sciences are 
not exact as are physics and chemistry, although they have certain 
fairly exact phases. Perhaps a sample of living conditions will make 
clear what I mean. For many of us there is a great pleasure in 
getting out into the field and observing life as it is lived there. Some 
three decades ago when I was young and vigorous, I spent a well- 
remembered brief period in the Canal Zone in Panama. There on 
Barro Colorado Island I drove my share of a set of long spikes into 
a tall tree, with Negro workmen doing the others. The tree rose out 
of a dense tropical rain-forest and towered above the forest canopy. 



Biology 239 

The spike ladder enabled me to climb through marked changes in 
climate. There was almost no air movement at the forest floor; it 
amounted to less than a mile a day during the windy dry season. 
Overhead, in the forest canopy, the wind moved at the rate of ten 
miles a day; farther overhead, entirely above the canopy, it was prob- 
ably moving 24 times that fast. 

The temperature was nearly or quite the same at top and bottom 
of the tree at night or under dense clouds. In the canopy, and in 
the bigger sunflecks on the ground, it ranged at least 18F. higher 
during the day than it was in the heavy shade at the tree's base. 
The evaporation rate was some six times as fast in the tree tops as 
on the ground, and the intensity of light in and above the tree 
tops ranged from 25 to 500 times that on the forest floor a hundred 
feet below, or more. 

The majority of animals in that tropical rain-forest and there are 
large numbers of many different kinds of them live on the forest 
floor where, apart from the easily avoided sunflecks, the environment 
is remarkably constant. Ants are the most characteristic animals pres- 
ent, though not nearly so exciting as jaguars or monkeys. The upper 
forest has the hazards of life in the trees added to the much more 
extreme daily changes in living conditions. I was distinctly disap- 
pointed both in the numbers of individuals and in the numbers of 
forms to be found higher and higher in the tree. Again ants were 
most numerous. Mainly they belonged to different species from 
those on the ground. 

It is hard work collecting animals in the upper, or monkey, region 
of the forest. They can be shot, using dust shot for insects, birds 
and small lizards, for example. Even then they are not yet in hand 
and may never fall through the thick foliage to the ground. I well 
remember a sleek, short-legged, apparently slow-moving, lizard that 
repeatedly slipped away from my free hand. He handled himself 
very well as did other much larger lizards, birds and monkeys. I was 
at a disadvantage moving cautiously among the branches some 70 
to 80 feet above the ground. I felt a distinct handicap in my lack of 
a prehensile tail. Certainly the animals are different in the different 
forest levels, as strikingly different as are the immediate environ- 
ments in which they live. 



240 What Is Science? 

Plants and animals, especially animals, reveal many of their ecologi- 
cal relations by their behavior toward both living and nonliving 
things about them. We have already seen that in certain of their 
reactions they may resemble physical and chemical systems, both in 
principle and even in many details. Also they may show more com- 
plicated types of behavior too complicated to have been analyzed 
as yet into physical and chemical phases. Superficially viewed, the 
reaction of the horseshoe crab moving away from light illustrates 
both aspects, until one tries to break the diagrammatic movement, 
which resembles that of a guided missile, into its finer elements, with 
the legitimate goal of trying to find the simplest nerve-muscle com- 
ponents of the behavior complex. As yet, the best efforts yield only 
vague approximations at this level. Neither the machine nor the 
supermachine emerges too clearly. 

Consideration of the behavior of plants and animals extends far 
beyond the limits usually set for ecology and, in fact, stretches the 
conventional limits of biology, not only toward the basic sciences, 
but also toward philosophy. One rather complete outline of the con- 
tent of animal behavior recognizes a primary division into unlearned 
behavior on the one hand, and learned patterns on the other. These 
two major types of reactions have many fundamental similarities. 
Unlearned patterns do not usually run their courses automatically 
and mechanically. In addition to fixed and unchanging components, 
given as a result of some inherited tendencies released by a proper 
stimulus, even inherited behaviors contain a variable element that may 
be more or less adapted to the particular situation. Horseshoe crabs 
crawling fixedly away from light adapt to the inequalities of the 
surface over which they crawl. Conversely, a certain amount of in- 
herited behavior enters into every form of learned activity. 

An act is at one and the same time normally a function of un- 
learned or constant behavior and of learned or variable elements. In 
its more complex phases the inherited, constant activities are called 
instinctive, which is a much-abused word with many different shades 
of meaning. Under many conditions the variable, learned phase may 
produce an appropriately modified reaction that fits surrounding con- 
ditions; under other circumstances it results in an unexpected re- 
sponse to the given situation. 



Biology 241 

Analysis of an action into these two parts lacks reality. Constant 
and variable activities must not be taken as two more or less opposed 
natural agencies pulling the organism now in this direction, now in 
that, as they battle for supremacy. Rather, they are two different 
phases of the same whole. In inherited, innate, instinctive reactions 
the "constant" elements are greater than the "variable" ones; in 
intelligent behavior the relation is reversed. 

Two bits of instinctive behavior that I saw myself may be helpful 
and interesting. Years ago, near the Marine Biological Laboratory at 
Woods Hole on Cape Cod, I was trotting back from a noontime 
swim in a hurry for food when I saw a wasp dragging a caterpillar 
across the uneven surface of the dusty road. The caterpillar was 
alive but had been stung into a complete paralysis. 

I stopped to watch. The wasp turned before she reached the rude 
sidewalk. She passed near a low sturdy weed up which she climbed 
and draped the limp caterpillar over a low fork some few inches 
from the ground. 

All this time the wasp was being followed by a small tachina fly, 
which would lay her own egg or eggs on that of the wasp. I knew 
that the wasp would eventually bury the caterpillar and lay an egg 
on it. The egg would hatch into a grublike larva, which would eat 
the still living, paralyzed caterpillar, only to be eaten itself by the 
grubs of the tachina fly. 

I knew all this, and also knew that wasp and fly were reacting 
according to inherited behavior patterns, and that there was high 
probability, amounting almost to certainty, that neither had any 
foresight of the outcome. 

The wasp descended from the weed and proceeded a few feet to 
a small burrow, which was a fraction of an inch wide and about 
that deep. She had dug the burrow before stinging the caterpillar. 
She entered and enlarged the little cavity, digging vigorously, and 
throwing the dirt, like a dog, out between her hind legs. 

After a short time the wasp left the enlarged burrow and returned 
along the way she had come. However she did not remember the 
weed-climbing incident and did not locate the caterpillar immedi- 
ately. Meantime the tiny tachina fly had stayed near the caterpillar 
instead of following the wasp on her digging activities. Finally the 



242 What Is Science? 

wasp found the weed, climbed it, brought down the caterpillar and 
renewed her slow progress to the burrow. Now the tachina fly fol- 
lowed, again keeping about a foot to the rear. 

The wasp dug a bit more, dragged the caterpillar into the burrow, 
and deposited her egg. At that moment the tachina fly darted for- 
ward, dove into the burrow, presumably laid her egg or eggs, 
emerged, and flew away. The wasp filled the hole, leveled off the 
nearby ground and she, too, flew away. 

In another instance, in a different part of the country, after the 
wasp filled the burrow she leveled off the ground for a few square 
inches making the spot similar, so far as I could see, to the bare 
ground elsewhere except for its being darker from the moisture which 
would soon dry. Still she hovered near giving the impression that she 
was not yet through. After a short time she settled down on a fallen 
cluster of three pine needles still held together as they had grown on 
the tree. It took hard work for her to drag the bundle of needles to 
the drying site of the burrow where she deposited them near the 
center of the small litter-free spot. The wasp then flew away as though 
entirely finished. The place where she had deposited the pine needles 
looked as casually littered as was the ground nearby. 

All these complicated patterns were excellent examples of un- 
learned behavior, both by wasp and tachina fly. Yet mixed in with in- 
stinctive responses, which were dominant, there was evidence of ad- 
justment to the existing irregularities in the surface of the dust, on 
the part of the crawling, burdened wasps. They each made changes 
in the size of the burrow, and in the behavior centering upon the 
weed or pine needles. The long pause of the tachina fly near the 
caterpillar hanging draped over the weed was similarly a distinct 
variation from her normal, simple instinctive pattern. 

Such complex examples of unlearned behavior are well known. 
Simpler patterns are much more common and are shown even by 
single-celled protozoans, which also give evidence, at least in certain 
cases, of the beginnings of learned behavior. The unlearned, in- 
herited patterns evolved as did structure; they are deeply ingrained 
I sometimes say they are built in and can be modified only by 
evolution, whereas learned responses are much more plastic. Both 



Biology 243 

occur in the communal reaction of animals to each other, among 
nonhuman forms, as well as in man. 

The subsocial and social life of animals shows two major tenden- 
cies: one toward aggressiveness, which is best developed in man and 
his fellow vertebrates; the other toward unconscious, and in higher 
animals, toward conscious co-operation. With various associates I 
have long experimented upon both tendencies. Of these, the drive 
toward co-operation, for reasons that will soon become apparent, is 
the more elusive and the more important. 

Aggressiveness in the defense of territory is widespread, particularly 
among vertebrates. Many fishes show a high development of territo- 
rial defense, especially in the breeding season. Both intruding and 
defending fish seem to recognize boundary lines. The animal in its 
own territory normally fights harder than when it is the invader; 
further, its aggressiveness tends to become less spirited with increas- 
ing distance from its own territorial center. A few amphibians, many 
lizards, birds and mammals, including man, defend the boundaries 
of areas they occupy. 

Fighting is often involved though animals of diverse kinds use 
warning displays both to prevent invasion of their territories and to 
repel an invader. The singing of location-holding male birds fre- 
quently has this effect, and song may be substituted for actual com- 
bat, somewhat as bands of howling monkeys engage in howling con- 
tests when near their common borderline. 

The male tends to be more active than his mate in territorial de- 
fense; often she takes no part at all in such activities. Aggression of 
this kind is definitely related to that resulting in dominance hier- 
archies. 

Social orders of dominance are clearly developed in many small 
flocks of hens. Frequently hen A pecks B, both peck C, and so 
through the flock, without B pecking back at A, or any of the hens 
pecking her superiors. The individual with lowest rank pecks none 
and is pecked by all. Variations also occur. In the most common one, 
A pecks B, B pecks C, and C, surprisingly enough, pecks A, thus 
forming a pecking triangle. The higher rank between a pair of hens 
is won by an individual simply standing her ground when meeting a 



244 What Is Science? 

stranger, or by threatening, or, more rarely, by winning a fight. Once 
established the order tends to persist. 

I have studied nip orders in fish, peck orders in several species of 
birds, fight orders in lizards, mice, and in dogs, hook orders in cows, 
and various kinds of dominance orders in humans. In some species, 
supremacy is gained now by one and now by the other individual of 
a given contact pair. (After many pair contacts, it is possible for the 
observer to know which one wins out most frequently.) In other 
species the dominance is absolute. 

The peck orders among hens give a fair illustration of the self- 
centered phase of group biology and show one form of the individual 
struggle for existence. This kind of social organization illustrates an 
important part of Darwin's theory of evolution. 

High position in the social peck order confers privileges. We 
know that top-ranking animals feed more freely, and that high- 
ranking males of rhesus monkeys, sage grouse, common chicken, 
and other species have more ready access to females. Low social rank 
may lead to semistarvation in common domestic hens, to reduced 
sexual drive among cocks, to being forced out of coveys in California 
quail. Among many species, it forces the low birds in the peck order 
into inferior territories. 

With some animals, high social rank carries responsibilities for 
leadership, or for guard duty; in other instances no correlation be- 
tween social rank and social service has been found. With many 
other animals, as in groups of men and women, the true leaders do 
not necessarily hold high social rank. The leadership-followership set 
of relations are more nearly related to co-operative tendencies than 
they are to aggression. 

Aggressive behavior, for all its dramatic interest and frequent im- 
portance, is not basically as significant as are the group-centered 
tendencies toward co-operation, which may well be called proto- 
co-operation. Among lower organisms, the beginnings of co-operation 
are entirely nonconscious. Natural co-operation in its simpler forms 
implies merely that the relations among cells forming a plant or 
an animal, or among individuals within a group, are of more help 
than harm. 



Biology 245 

At all levels in the animal kingdom, from the protozoans to in- 
sects and to man, and under a variety of conditions, there is safety 
in numbers, always providing that the number is not excessive. The 
dangers of overcrowding are well known and can easily be shown. 
The equally real dangers of undercrowding are often less easily seen. 
Mass protection from cold is common, especially among warm- 
blooded animals. Grouped animals protect one another from many 
poisons and from other harmful chemicals. A concrete example of 
the greater safety in larger as compared with smaller numbers may 
be helpful. Among college students at X, or perhaps better F, uni- 
versity, a group of students who drive out to a drinking party may 
suffer little or no harm if the party is large, and the supply of alcohol 
is not too generous. In contrast, a few students consuming the same 
amount of alcohol run grave risks of automobile accidents on the 
way home, not to mention other adverse effects that are possible. 

Living sponges literally can be torn cell from cell, as by squeezing 
them through the meshes of a common linen handkerchief. Provid- 
ing enough cells are present, those falling in the water near each 
other fuse and grow into new sponges. In one carefully tested case, 
clumps of about 2000 cells formed new sponges; those of 40 to 500 
cells died. Somewhat similarly, if a natural population is decreased 
until only a few remain alive, the species is in danger of dying out 
in that locality unless others move into the area from elsewhere. The 
species may become extinct even though in theory enough animals 
are present to reproduce themselves and persist. The heath hen is 
a good example. It died out completely in 1932 after a long last 
stand on Martha's Vineyard off Cape Cod. 

Many animals and plants can produce a change in unfavorable 
surroundings, if enough are present, so that the group can survive. 
Some may die off in the process, but by dying they may produce such 
changes that those living with them, or others following, survive 
better and even thrive when they could not do so under the initial 
unchanged conditions. 

It may well be that the first living particle in the world lived only a 
moment, or at any rate for a very short time. In disintegrating it 
could have neutralized a part of the poison that killed it. As a result, 



246 What Is Science? 

and for a brief interval, that particular tiny niche might have favored 
the continued existence of the next living particle to be formed 
therein. 

Some vital processes are slowed down by increased numbers so 
that all present have a better chance to live. Spermatozoa of many 
sea-dwelling animals afford an example. Marine forms often have 
separate sexes that shed eggs and sperm into the sea where fertiliza- 
tion and development occurs. Scattered spermatozoa lose their ability 
to fertilize eggs sooner and live for a shorter time than when they are 
massed together. 

Many biological processes carry on at a higher rate of speed in the 
presence of populations of optimal size and density. Such activities 
are slowed down both in overcrowded and in undercrowded popula- 
tions. The length of time between first divisions in fertilized sea- 
urchin eggs follows this rule. Various kinds of protozoans show in- 
creases in the rate of sexless reproduction, if the right number are 
present, rather than too many or too few. Many divide more fre- 
quently when two asexual individuals live in the same small really 
tiny laboratory niche as compared with the rate shown by their 
isolated sisters in the same amount of liquid. Sexual reproduction 
may well have evolved from such a beginning. 

Some protozoans live in colonies. These could hardly have evolved 
from solitary forms unless the colony of cells that remained attached 
together after division had shown the beginnings of co-operation to 
a greater extent than did the ancestral cells, which were scattered 
singly. The evolution of the many-celled higher animals from the one- 
celled protozoans was probably based on similar relationships. 

Each advance in complexity of plants and animals arose through 
the natural selection of an increased ability of the individual elements 
(cells or organs) of the evolving stock to co-operate; the greater natu- 
ral co-operation came first, and then it increased by selection follow- 
ing variation. 

Charles Darwin recognized that a relatively large population is 
highly important in evolution by natural selection. Today there is 
growing evidence that evolution proceeds more rapidly in popula- 
tions of interbreeding animals that are neither too small nor too 
large. It takes place fastest when a population is broken up into 



Biology 247 

small breeding units, which are not completely separate from each 
other. Then, if a favorable variation occurs in one group, emigrants 
can carry the improvement to neighboring small units. Given time, 
and there is almost an endless supply of time in the world, a useful 
adaptation can be carried through the whole set of partially isolated 
groups. 

The dependence of living beings on one another is shown by the 
repeated observation that all living things, from the simplest to the 
most complex, live in loosely knit communities; this is plainly seen in 
coral reefs or oyster beds, as well as in colonies of ants and among 
men. Further, the evolution of truly social animals has taken place 
independently in such widely separated divisions of the animal king- 
dom as insects and man. Societies could hardly have arisen so fre- 
quently and in groups of such unlike forms if there were not a strong, 
underlying level of automatic unconscious, proto-co-operation among 
animals. In nature, no animal is solitary throughout its life history. 

As has already been stated, there are two types of social or sub- 
social interactions among animals: the self-centered drives that lead 
to individual advancement or self-preservation, and the group-cen- 
tered, more or less altruistic drives, which lead to the welfare and 
protection of the group as a whole, or to the persistence of a part 
of it even with the loss of many individuals. 

The germ of the concept of natural co-operation, along with that 
of natural selection, can be traced back to the early Greeks. Because 
of the idea of natural selection, and owing to the interpretations of 
Darwin's followers in the late nineteenth century, the self-centered 
drives of natural selection, with all nature pictured as being red in 
tooth and claw, stole the show for several decades. Today, balance is 
being restored. The picture that emerges from recent studies of 
social biology is one in which co-operations and their opposite, dis- 
operations, both exist. Both self-centered and co-operative forces occur 
in nature, and each plays an important role. 

The question arises insistently as to which of these opposing tend- 
encies is more basic and powerful. A well-considered answer must be 
based on both short-run and long-run effects. I know no experiment 
that tests such matters directly. After much thought, and all the 
reading and research that I have been able to do, it is my mature 



248 What Is Science? 

conclusion that co-operation is more important. The balance between 
co-operative tendencies and those that are disoperative may be rela- 
tively close. Co-operation loses under many conditions. In the long 
run, however, the group-centered drives are at least slightly stronger. 

If co-operation had not been the stronger force, the more com- 
plicated animals, whether insects or birds, or mammals, could not 
have evolved from the simpler ones, and there could have been no 
men to worry each other with their distressing and biologically foolish 
wars. Despite many known appearances to the contrary, human co- 
operative drives are as firmly based on an animal ancestry as are 
the disoperative ones that we think of as human evil. Our tendencies 
toward co-operation, such as they are, are as innate as our tendencies 
toward thinking. We could do well with more of both. 

Now I come to the more delicate part of the task that I have under- 
taken. In order that my possible personal bias, if any exists, may be 
apparent, I should say that I am a citizen of the United States of 
America, with generations of American ancestors. Further, I am both 
a mature biologist and a working, though highly unorthodox, member 
of a religious organization. As I see it, our present-day European 
style of civilization is based primarily on religion, on other forms of 
tradition, and on science. The arts furnish color and interpret human 
behavior and thinking. Philosophy busies itself, or should, with try- 
ing to understand and explain the whole. The functioning of modern 
civilization, if it is to be properly effective, calls for the co-operation 
of all these elements. 

Today, as in the past, religion wastes valuable time and energy 
quarreling with science about the relative importance of each, and 
over the proper division of opportunities and recognition, a quarrel 
that scientists now largely ignore. Philosophy invades the fields of 
both. Too often art becomes cynical and irresponsible, and philos- 
ophy scolds all and sundry, sometimes in no friendly voice, for the 
general unwillingness to let philosophy direct the whole. 

Philosophy insists, even yet, on its discredited, age-old claim of 
having a special short cut to knowledge. Certain philosophers scold 
science, the most recently revitalized influence in civilization; and 
strong elements of modern religion, having attempted to use science 



Biology 249 

to establish their claims, try to carry on alone in some of the most 
vital activity and thinking of our times. 

Here, as elsewhere in human efforts, it is easier for closely knit ele- 
ments in a situation to develop frictions among themselves than it is 
to disregard relatively petty internal troubles and make common 
cause against serious opposing forces. The enemies of the better as- 
pects of our none-too-perfect civilization are strong enough to require 
united efforts from the arts, philosophy, science, and religion if they 
are to be properly met. Perhaps plain speaking from a somewhat 
aberrant friend of all these elements of modern social life may be 
helpful. 

Religion has much to learn from science in objectivity, in willing- 
ness and courage to follow evidence faithfully, and even in judging 
what constitutes valid evidence. Particularly religion can learn from 
science the advantage of giving up the thundering "Thus saith the 
Lord" in favor of the more humble, and essentially more effective 
summary of "This appears to be the evidence/' In short, religion can 
profit by becoming intellectually more sound without losing for a 
moment its proper emphasis on the deep emotions of man. And 
science has much to learn from religion. I mean from real religion, 
not from the semi-science of theology, which, too often, consists 
mainly of esoteric playing with words or the juggling of selected ideas. 

Religion is ill-served by past and present emphasis on mystical and 
supernatural improbabilities. I hesitate to use the word "God" be- 
cause of the wide variety of meanings attributed to it. Even so, "God"^ 
is a possibly permissible name, if one must have a name, for the 
personification, or, perhaps better, the abstraction, of all the best that 
mankind has been able to think, and feel, and do, of all the beauty we 
have created, together with all the natural beauty we can appreciate, 
and of all the love anyone has been able even to imagine. Such a 
conception transcends tradition and mere emotion; it has both 
power and dignity. God may be much more than has just been in- 
dicated; I do not know. This statement is by no means final; how- 
ever, it is as close an approach to the truth as my knowledge of real 
evidence permits me to make at the present time. 

Science has much to learn from a religion with some such concept 



250 What Is Science? 

of God, a religion characterized by social consciousness and honest 
thinking, combined with propaganda of the deed. More specifically, 
we scientists can profit by being more humble in the face of our im- 
mense ignorance even within our own fields of special study. We can 
also tone down our excessive pride in the discoveries we have been 
able to make, which are small in the face of the unknown. 

Scientists can profit by a frank admission of awe and admiration 
for the great beauty of the objects and processes that we study, the 
charm of which often escapes us because of our focusing on detail. 
We will profit by being less certain that the more unattractive the 
interpretation, the closer the approach to truth. We will gain in the 
long run by working in our chosen fields more quietly. Science and 
mankind, and religion, too, for that matter, would profit if all men 
would live closer to the ideals expressed and practiced by the more 
devoted men of religion, and science. 

I would make these suggestions in stronger language were it not 
for the fact that from a fairly wide and close relationship with many 
kinds of people, individual exceptions aside, scientists in general, and 
biologists in particular seem to be the best people I know. This may 
be an expression of prejudice based on similarity of experiences and 
on congeniality of temperament. I am inclined, however, to regard 
the differences between my scientific and my other friends as real, 
and to attribute it to the training furnished by effective exposure to 
the methods of science. 

The biological sciences impose an especially effective discipline in 
that they combine an impressive need for precision in detail with a 
large content of mystery. The combination is the more effective in 
that a mistake in judgment concerning the mysterious, unanalyzed 
elements often is exposed relatively soon by some new, more pene- 
trating measurement. The continuous checking of ideas against 
sound, objective evidence does something to make conscientious fol- 
lowers of the scientific method essentially more honest and less given 
to self-deception than are those skilled in the manipulation of ideas 
or words. 

Despite my belief in the goodness of my fellow biologists, I admit 
that even study in laboratory or field, including good research work, 
does not necessarily bring forth some of the higher types of altruism. 



Biology 251 

When asked to recommend someone to teach biology in a deserving 
though struggling Negro college in the United States or in Africa, or 
in remote ill-equipped, much-needed laboratories in China or India, 
I have learned to turn to students with a strong religious background 
for those with vision enough to see that the opportunities may, in the 
long run, repay the sacrifices. 

Let us take another approach. No one passes much time without 
being reminded that we are living in a world and in a country where 
international relations are based on war, or on threats of war. We 
need to examine frequently our responsibilities under current condi- 
tions for, like other animals, we men and women do not live in a 
vacuum insulated from the impacts of our time. For most, particu- 
larly for those who arc fully mature, we should continue at our pres- 
ent jobs, or at something closely similar. The younger generation 
needs as many steady points of reference as possible. This is apparent 
when they come, as many do, to talk themselves quiet in the pres- 
ence of a sympathetic, calm, older person in whom they place some 
confidence. In addition to helping maintain intellectual honesty and 
competence, we need to give full play to all activities making for 
emotional maturity and stability. We need also to know that the nat- 
ural human fate is not to engage in a struggle for existence based on 
man's fighting tendencies combined with those of our animal an- 
cestors, softened only by slight checks imposed by more or less artifi- 
cial rules for human conduct. 

The biological support for the doctrine of the inevitableness of 
war is now opposed by strong evidence indicating that the idea of a 
ruthless struggle for existence is not the whole, or even the major, 
teaching of current biology in regard to social philosophy and social 
ethics. This newer evidence, which I have outlined above, does not 
cast doubt on the existence of the human vices of pride, covetousness, 
lust, anger, gluttony, envy, and sloth. Neither does it remove indica- 
tions that these find natural roots in behavior of nonhuman animals. 

The newer biology strengthens decidedly the older evidence for a 
biological basis for the human virtues of faith, hope, and love. It 
supplies renewed indications that men have also inherited and im- 
proved on these tendencies through a long evolution. Modern find- 
ings strongly suggest that, as in all animal behavior, with its combina- 



252 What Is Science? 

tion of learned and innate elements, the present high state of the 
seven capital sins just named is an expression of man's learned devil- 
ishness as well as of his inherited behavior patterns. The former be- 
lief that these sins are man's inevitable response to his inherited na- 
ture is no longer tenable. 

We have come a long way in the present chapter, all the distance 
from considering how life may have originated, exclusively as a natu- 
ral event, to a glance at some current phases of human thought and 
action, still without bringing in anything supernatural. It is impres- 
sive to realize that life has evolved from a barely living molecule 
until one animal man can think out a rough working pattern of 
his whole world and of much of the universe. The evidence is not 
all in and our ideas are far from final. Much research and thinking 
needs to be done, but the prospect for further progress is hopeful. 
Man's glimpse, in the large, of the advance from the first living parti- 
cle to the best human thinking is the most important insight in 
biology, or in all of science. 



EVOLUTION AND 
GENETICS 

JULIAN HUXLEY 



about 

Julian Huxley 



Julian Huxley, brother of Aldous, son of Leonard and grandson of the 
famous Thomas Henry Huxley, was born in London, June 22, 1887. 
He received his early education at Eton and Balliol College, Oxford, 
where he specialized in zoology. From 1912 to 1916 he taught at the 
Rice Institute in Houston, Texas, and in 1919, after military service 
in Italy, returned to Oxford as a fellow of New College and Senior 
Demonstrator in Zoology. He held the chair in zoology at King's 
College, University of London, 1925-1927, and the Fullerian profes- 
sorship of physiology at the Royal Institution, 1926-1929. In the 
1930s and '40s Huxley was active in many different scientific and 
educational enterprises, ranging from supervision over the making of 
biological films and service as secretary of the Zoological Society of 
London to membership on the General Committee of Lord Hailey's 
African Survey and adviser on East African education. Recognition 
of his contributions to education and his exceptional devotion to 
the cause of social betterment came with his appointment as first 
Director-General of the United Nations Educational, Scientific and 
Cultural Organization (UNESCO) in 1946, a post he held for two 
years. 

Huxley s researches in biology have established his position as one 
of the world's foremost authorities on evolution. (He is since 1938 a 
Fellow of the Royal Society and has received many other academic 
awards.) He combines broad scientific knowledge and scholarsliip 

254 



about Julian Huxley 255 

with a profound critical and philosophical faculty. This cast of 
thought is displayed in his scientific papers and books no less than in 
his prolific writings for general audiences. Among his publications are 
Essays of a Biologist (1923), Essays in Popular Science (1926), 
Animal Biology (with J. B. S. Haldane) (1927), and The Science of 
Life (with H. G. and G. P. Wells) (1929), all of which show his 
exceptional gifts as a popularizer of science; The Captive Shrew and 
Other Poems (1932); Evolution: The Modern Synthesis (1942), a 
masterly scientific work surveying great masses of data and various 
theoretical aspects of the subject and unifying them into a compre- 
hensive interpretation; Scientific Research and Social Needs (1934); 
TVA: Adventure in Planning (1943); Man in the Modern World 
(1947); Heredity, East and West (1949). 

Now 68, Huxley's energy seems rather to increase than to diminish 
as he grows older. In 1953-4 he made an eight and a half month trip 
to Hawaii, Fiji, Australia, Java, Bali, Manila, Singapore, India, Ceylon, 
Pakistan, Iraq, Persia, Syria and Lebanon. He returned from this jour- 
ney, which was punctuated by innumerable lectures and conferences, 
to greet the publication of his book, From an Antique Land, an ac- 
count of his travels in 1948 in the Middle East, with sections on 
its history and archaeology, and his own handsome color and black 
and white photographs. 

In 1954, also, he finished a long scientific paper on "Polymorphism 
and Evolution," started a new book on his most recent journey, and 
set off again on a visit to the United States to speak at the Columbia 
Bicentennial and to lecture all over the country on "Evolution and 
Human Destiny" and similar subjects. 

Huxley was married in 1919 and has two sons. In light of his im- 
mense literary and scientific output, his professional travels and many 
other duties, it is hard to imagine he has any time for recreations; 
nonetheless, he lists several in Who's Who whether wistfully or as a 
report of activities pursued is not indicated including bird-watching, 
swimming and "travel." 



EVOLUTION AND GENETICS 

JULIAN HUXLEY 



Life can be studied from two distinct points of view. These can be 
rather crudely summed up in the two words mechanism and process, 
or by means of the two questions "How do organisms work here and 
now?" and "How do organisms change in the course of time?" Most 
studies in anatomy, morphology, physiology, systematics, and ecology 
are trying to find answers to the first question, while those in evolu- 
tion, embryology and most of genetics are concerned with the second. 

In what follows I shall be discussing various aspects of this second 
question: how living matter reproduces itself, how it varies, how it 
becomes organized into different forms, how it is acted upon by 
selection, and how it becomes transformed in the course of time 
in other words, genetics in the broad sense, together with evolution 
regarded as a process. 

The work of the last forty years has made it clear that these two 
fields are complementary. We cannot understand evolution unless we 
understand the process of hereditary transmission, and we shall not 
transcend a limited and static view of the mechanism of heredity un- 
less we study how it may be altered in the course of evolutionary time. 

This was not always so. Biologists could not begin exploring the 
evolutionary implications of genetics before the fact of evolution had 
been established, nor could they begin to understand the bearing of 
genetics on evolution before the mechanism of heredity had been dis- 
covered. The first took place less than a century ago, the second less 
than half a century. 

256 



Evolution and Genetics 257 

I shall therefore start by treating the two subjects separately, be- 
ginning with genetics. Genetics is the science concerned with heredity 
the way in which life and its characteristics are transmitted down 
the generations. It is really extraordinary how many superstitions and 
false notions prevailed in the past on this subject. 1 Thus in antiquity 
it was believed that quite highly organized animals such as flies, bees, 
frogs, and even mice, could be "spontaneously generated" out of mud 
or putrefying matter in other words that there was no mechanism 
of material transmission of living substance from one generation to 
the next. This notion was killed, so far as higher animals go, in the 
seventeenth century by Redi, the Florentine naturalist, physician and 
poet, who proved that maggots did not appear in meat when it was 
screened to prevent blowflies laying their eggs in it; but it survived 
in regard to microscopic organisms like infusorians and bacteria until 
dealt its deathblow by Pasteur barely a century ago. 

Another widespread superstition was that maternal impressions 
could influence the characters of the offspring. In the Bible, Jacob is 
stated to have caused the birth of piebald and spotted sheep and goats 
by making the expectant mothers look at "pilled wands" twigs on 
which stripes and patterns had been cut. In 1920, my wife, who was 
carrying our first child, was warned by our maid not to look at a large 
and ugly fish in the aquarium at Plymouth for fear that this should 
influence the baby's appearance. 

An even more widespread error is the belief in the inheritance of 
"acquired characters." This phrase, by the way, proves somewhat of 
a stumbling block to many laymen: they ask, not unreasonably, 
whether all new characters that appear in evolution are not "ac- 
quired." However, the point is a purely semantic one. "Acquired char- 
acters" in this connotation are defined as characters acquired by the 
individual during its lifetime as the result of environmental agencies, 
or of use or disuse of organs. Characters of the former type include 
the tanning of white men's complexions by sunlight, the excessive 
vegetative growth of green plants in nitrogen-rich soils, the goiter in- 
duced by lack of iodine, or the succulence of plants in saline condi- 
tions; among those of the latter are the enlargement of muscles by 

1 See C. D. Darlington's recent book The Facts of Life (1953) for a pungent and 
learned account of prescientific myths and theories of reproduction and inheritance. 



258 What Is Science? 

hard exercise, learning, the improvement of sensory discrimination by 
practice, and the growth of tendons in relation to the mechanical 
stresses they are called on to support. 

The theory of evolution by means of the inheritance of acquired 
characters is often called Lamarckism, after the great French natural- 
ist Lamarck, whose main works were published early in the nineteenth 
century. Although he believed only in the evolutionary importance of 
characters individually acquired through use and disuse, as the result 
of deliberate effort (or lack of it), the term Lamarckism is commonly 
extended to cover the inheritance of all "acquired characters." 

Today we know that acquired characters in the above sense are 
never inherited, and indeed are not heritable. Any character of an 
individual animal or plant is always the joint product of heredity and 
environment. If there is a sufficient alteration either of the hereditary 
constitution or of the environmental conditions, the character will be 
altered. Furthermore, the hereditary constitution, as we shall see, con- 
sists of a highly elaborate system of material self-reproducing units or 
genes, each with its own specific chemical nature. During early life, 
this system interacts with its environment to set in train the processes 
of development, and these in turn give rise to the individual organism 
with all its visible "characters." Thus any direct effect of environ- 
ment upon a character is exerted on a late stage of a developmental 
process, not on the genes underlying it. For instance, sunburning acts 
on the processes of pigment-formation in a man's skin, and cannot 
possibly affect the genes in the sperm-producing cells of his testes, since 
there is no mechanism for the transfer of specific or self-reproducing 
material from any organ of the body to the reproductive organs. 

Indeed, it might have been deduced on general grounds that de- 
vices would have been evolved to prevent the hereditary constitution 
from being affected by environmental changes; for the primary func- 
tion of heredity is to transmit a standard self-reproducing system 
which is adapted to the average conditions of the species' environ- 
ment. If every extreme of hot or cold, of dry or wet, were able to alter 
the genes, the standardization would be lost and the orderly system 
would be disorganized. 

We now know that a few environmental agencies can affect the 
genes directly. But these are all of particular potency, like X-rays, or 



Evolution and Genetics 259 

ultraviolet radiation, or a few special chemical substances; and what 
they do is to cause the genes to mutate, by altering their chemical 
structure, with consequent alteration of their effects on develop- 
ment. No case is known where the effects of any environmental agency 
on an individual character are the same as those which it may cause 
the gene to exert by making it mutate. 

As a result of the new point of view made possible by our new 
knowledge of the mechanisms of reproduction, heredity, and develop- 
ment, biologists have largely ceased using the phrase "acquired char- 
acters." 2 Instead they speak of such characters as modifications (of the 
individual), and classify visible variations into two radically different 
types those due to modification in this sense, and those due origi- 
nally to mutation, in the sense of an alteration in the genes. 

In passing, this modern approach enables us to dismiss the old 
question of whether heredity or environment is the more important. 
The answer is neither; for both are essential, though in particular cir- 
cumstances one or other of the two components may be more ef- 
fective. Thus if environmental conditions are kept uniform, as when 
a sample of seed is grown in a plot of uniform soil treated with the 
same fertilizers throughout, any differences in the resultant plants will 
be due to hereditary differences in their genetic constitution. Con- 
versely, if heredity is made uniform, by using seed from a pure line, 
any differences in the crop will be due to environmental differences, 
in soil or cultivation or fertilizer. 

Normally, of course, neither heredity nor environment will be uni- 
form, and then careful analysis will be required to discover what part 
of any difference between individuals is assignable to differences in 
heredity and what to differences in environment. This applies, for in- 
stance, to human statute or scholastic ability, or to differences in 
yield between crop-plants grown from imperfectly purified seed in a 
variable environment. 

Another superstition prevalent among animal breeders is that of te- 

" In order to make the inheritance of acquired characters comprehensible (as well 
as to have some model for hereditary transmission in general), Darwin advanced 
his theory of pangenesis, in which he postulated the existence of minute living 
particles or "gemmules," which were supposed to be detached from all bodily tis- 
sues and then to be transmitted in heredity. Later research, however, showed that 
no such mechanism exists. 



260 What Is Science? 

legony, or the supposed influence of a previous sire on the offspring 
from a later mating. Although this is entirely groundless, it has led 
to many valuable female animals being rejected for pedigree breed- 
ing, because they had earlier been mated to "mongrels." 

These myths and errors have now been dispelled by the advance of 
knowledge. The basis for a scientific theory of heredity was laid 
when, during the mid-nineteenth century, it was finally established 
that reproduction always takes place by the development of a piece of 
living substance detached from the parent. Sexual reproduction in- 
volves the complication that two pieces of living substance in this 
case, single cells are detached from the two parents, and then unite 
to form one. The cells which thus unite are called gametes or marry- 
ing cells, and the product of their union (the fertilized ovum in higher 
organisms ) is called a zygote. 

The next step was the demonstration that the essential element 
handed down in reproduction consists of a set of visible cell-organs, 
the chromosomes, which in each species occur in characteristic shape, 
size and number. Elaborate machinery exists for ensuring that each 
time a cell divides, the chromosomes too reproduce themselves, the 
original set becoming doubled and then dividing so as to produce 
two identical sets, one of which passes into each daughter-cell: this 
is called mitosis. In the process called meiosis or reduction, which oc- 
curs during two cell divisions before the gametes (sperms and ova in 
higher animals) are produced, the number of chromosomes is reduced 
to half, so that the gametes are haploid, i.e., with one instead of two 
of each kind of chromosome. With the fusion of the gametes at 
fertilization, the double or diploid number of chromosomes is re- 
stored, so that the zygote possesses two complete chromosome sets. 8 

Thus although the contributions of father and mother to the off- 
spring (zygote) are extremely unequal in terms of cells (gametes) 
the tiny, tailed, active spermatozoon or sperm from the one side and 
the bulky, inert, and often enormous ovum or egg from the other 
yet they are equal in terms of chromosomes, each providing one com- 

In a few cases, e.g., the sex chromosomes, a chromosome-pair may be unequal, 
one member being reduced or absent in one sex. Thus in our own species, men 
have one large (X) and one smaller (Y) sex-chromosome, while women have two 
equal X's. 



Evolution and Genetics 261 

plete haploid set. Since observation shows that fathers exert as much 
effect as mothers on the nature of their offspring, the chromosomes 
were thus revealed as being almost certainly the organs of heredity, 
or at least as its material basis. 

This self-reproducing system of chromosomes, operating by means 
of mitosis, meiosis and sexual union, was speedily shown to be a gen- 
eral characteristic of organisms, whether plant or animal, multicel- 
lular or unicellular, high or low in organization. In recent years it has 
been demonstrated in bacteria, and a simpler prototype of it appears 
to exist even in the submicroscopic viruses, on the borderline be- 
tween living and nonliving. 

Meanwhile in the 1860s, the first step was taken toward under- 
standing the invisible organization underlying this visible mecha- 
nism. The Abbe Mendel, by a series of brilliantly conceived experi- 
ments, made it clear that the inheritance of certain characters must 
be mediated by units factors or determiners of heredity which are 
transmitted from parent to offspring, and recombined in all possible 
ways in the sexual process. 

His results lay unheeded for 35 years. But as soon as they were 
rediscovered in 1900, biologists in many countries began to work 
along the same lines. Within a decade, it had been established that 
mendelian inheritance, depending on unit-factors and obeying Men- 
del's laws, was a general phenomenon; it occurred in every kind of 
animal and plant in which experimental breeding could be practiced; 
and today the list has been extended to include not only higher or- 
ganisms, but also mosses and molds, unicellular fungi like yeasts, the 
minute and simple bacteria, and even viruses. 

Furthermore, before 1930 it had been shown not only that men- 
delian inheritance was of general occurrence but that all inheritance 
(apart from a few cases of so-called cytoplasmic inheritance, by means 
of particles transmitted in the general protoplasm of the cell), was 
mendelian in other words dependent on the transmission and re- 
combination of discrete unit-factors. 

In the early days of mendelian research, attention was naturally 
focused on large or sharp character-differences, such as albinism, or 
red versus blue flower-color, or hornlessness in cattle, which were 
easy to distinguish and to follow in inheritance; and for a time it 



262 



What Is Science? 



(two possible alignments 
of chromosomes) 




Diagram showing independent assortment of two pairs of chromosomes, 
A-a and B-b. Note that at the reduction division there are two possible 
alignments of chromosomes producing four types of gametes. By random 
union these produce the sixteen different chromosome combinations 
shown in the F g checkerboard. (From Principles of Genetics, by E. W. 
Sinnott and L. C. Dunn, by courtesy of McGraw-Hill Co., New York. ) 



Evolution and Genetics 263 



Spermatogonia 



Primary 
spermatocyte 

Secondary 
spermatocyte 




Oogonia 



Primary 
oocyte 

1st polar body 
Secondary oocyte 



2nd polar bodies 
Mature egg 



First cleavage 

Diagram of spermatogenesis and oogenesis in an animal. (From Principles 
of Genetics, by E. W. Sinnott and L. C. Dunn, by courtesy of McGrmv- 

HillCo. t New York.) 







Comparison between mitosis in the body cells and in the reduction divi- 
sion which precedes the formation of the reproductive cells. The individ- 
ual chromosomes are differently marked. In ordinary mitosis (upper row) 
it is evident that the chromatin is divided equally between the two daugh- 
ter cells (F left and right). In the reduction division (lower row) the 
chromosomes do not split but align themselves in pairs (C and D) and 
one member of each pair goes to each pole (E), resulting in the formation 
of two cells (F), each with half as many chromosomes as the body cells. 
These by a subsequent equational mitosis give rise to four functional 
gametes (G). (Modified from Sharp.) (From Principles of Genetics, by 
E. W. Sinnott and L. C. Dunn, by courtesy of McGraw-Hill Co.) 



264 What Is Science? 

was supposed that they alone were inherited in mendelian fashion. 
Later, however, it was found that mendelian factors were responsi- 
ble also for the inheritance of small differences and of so-called contin- 
uous variation, in which no sharp line can be drawn between the 
characters under investigation. 4 In most cases of variation in size, for 
instance, including human stature, there is a continuous gradation 
from small to large; and yet size differences are genetically determined 
by mendelian factors. 5 

In the inheritance of continuously varying characters, a number of 
factors, all or most of them producing quite small effects, combine or 
interact to produce a larger effect. What is more, such interac- 
tion between separate factors was discovered to be a general occur- 
rence: thus the two factors responsible for the very distinctive "pea" 
and "rose" types of comb in fowls, when both are present together, 
interact to produce a comb of quite a new shape, the so-called 
"walnut" type. Or again, the "hooded" pattern of rats, in which the 
foreparts and a stripe along the back are black while the rest of the 
animal is white, depends on a single mendelian factor. But the effects 
of this can be altered by a number of so-called modifying factors, 
some of which can combine to extend the black area over the white 
of the upper and even some of the lower surface, while others operate 
to restrict it to the head or even to the snout alone. 

The original idea of the early Mendelians like Bateson had been 
that each mendelian factor corresponded to some one distinct visible 
character; and in fact they often used the term unit-character, as if 
the characters and not the factors responsible for them, were directly 
transmitted in inheritance. However, the facts soon made this view 
untenable, and it was eventually realized that every visible character 
depends genetically on several or many separate mendelian factors. 
Thus the mendelian factors, or genes as they were later called, though 
they behave as separate and separable units in regard to their transmis- 
sion, interact and co-operate in regard to their effects on characters. 
Spatially they are like a row of beads on a string; but functionally 

4 Though it took the mendelians over a decade to discover this, Mendel himself 
had prophesied it in the 1860s. 

8 As previously pointed out, they are not entirely so determined, since environmen- 
tal condition (such as amount of food) may also affect size. 



Evolution and Genetics 265 

they combine to form a single organized system. This organized sys- 
tem we call the gene-complex. 

Meanwhile the important phenomenon of mutation had been dis- 
covered. New characters such as white eye-color in place of the nor- 
mal red in the fruitfly Drosophila appeared in breeding stocks of 
various animals and plants, sometimes in pure-bred strains and then 
proved to be inherited in mendelian fashion. It soon became clear 
that the mutant characters were due to changes taking place in the 
hereditary factors in most cases presumably slight changes in chem- 
ical constitution or molecular organization. 

Since the hereditary factors are self-reproducing, the mutated fac- 
tor will reproduce itself and be transmitted in its new form to later 
generations. 

"Spontaneous" mutation of this sort was found to be a general 
phenomenon, occurring in all organisms. It is, however, very infre- 
quent. The rate of mutation for most factors varies from much less 
than 1 to about 50 per million: thus the mutation producing severe 
hemophilia ("bleeding") in man occurs only in about 30 of every 
million eggs or sperm produced, though the gene concerned has one 
of the highest mutation-rates known. 

In 1927 Muller made the important discovery that mutations, in- 
cluding many of those occurring spontaneously, could be artificially 
induced by means of X-rays, and that the mutation rate was then 
enormously increased. Similar artificially increased mutation has later 
been produced by various other agencies. 

It soon became clear that all characters which are inherited in men- 
delian fashion owe their origin to past mutation. Mutation in fact is 
the source of all heritable variation, and therefore provides the raw 
material for evolutionary change. 

Mutation can be of various kinds. The commonest kind is gene- 
mutation, which alters the nature of single genes or hereditary factors; 
but there are also chromosome-mutations of various sorts, some in- 
volving rearrangement of parts within or between chromosomes, oth- 
ers involving the addition or subtraction of whole chromosomes, and 
still others the addition or subtraction of whole chromosome-sets. But 
all mutations are capable of self-reproduction, and all produce some 
effect on the characters or properties of the organism. 



266 What Is Science? 

In the second decade of this century a further decisive step had 
been taken. The genetic system composed of the hereditary units 
deduced from breeding experiments had been equated with the 
visible mechanism of the chromosomes, and the "unit-factors" them- 
selves had been identified as material particles tiny sections of the 
chromosomes, each with its own particular location in the system, to 
which the name of genes was given. As a result, whenever sufficient 
genes had been studied in breeding experiments, it became possible 
to make maps of the genetic system, showing the position of the va- 
rious genes in the different chromosomes. 

This was truly a spectacular achievement. But the most important 
points established were the facts that inheritance is participate in its 
nature that is to say, is mediated by the transmission of definite bits 
of self-reproducing matter and that it is co-operative in its operation, 
that is to say the separate hereditary particles or genes combine or 
interact to produce their effects, and are all organized into a single 
functional system, the gene-complex. With this realization, not only 
did genetics find a firm scientific basis, but the relations between 
genetics and evolution were put on a new and satisfactory footing. 
As discussed more fully later, R. A. Fisher, the English statistician and 
geneticist, in his great book published in 1930, the Geneticd Basis 
of Natural Selection, was able to draw the most far-reaching theo- 
retical conclusions from this central fact of particulate inheritance and 
the detailed data concerning its operation. 

Recently, considerable progress has been made in what is some- 
times called physiological genetics the study of how the genes oper- 
ate on the processes of development to produce their effects on the 
characters of organisms. 

Remarkable discoveries have recently been made concerning the 
chemical nature of the genes or, what amounts to the same thing, 
the chemistry of self-reproducing (self-copying) matter. The self- 
reproducing gene-units of heredity consist of a combination of certain 
kinds of protein with a particular sort of nucleic acid in which the 
nucleic acid seems to act as a sort of chemical template, enabling the 
gene to impose its own precise form and organization on the materials 
from which it builds up a copy of itself; and the essential capacity for 
self-copying seems to depend on a peculiar structural organization, in 



Evolution and Genetics 267 

which two identical chemical strings are intertwined spirally with eacl. 
other, making chemical connection by means of their side-chains, 
but with the two members of the double spiral running in opposite 
directions ("head to tail") instead of parallel. 

Genes must now be regarded as self-copying chemical molecules or 
super-molecules of very large size (with molecular weights of a million 
and over) and very great complexity of organization. Indeed, their 
organization is so complex that various external agencies, like X-rays, 
or spontaneous internal rearrangements, can produce slight altera- 
tions in it, such as a change in the number or position of the atoms 
in one of its numerous side-chains. If such an alteration is not too 
great, the gene will reproduce itself in the new altered form. It is these 
alterations that we detect as genetic mutations. 

The study of heredity is thus leading to discoveries about the mech- 
anism of self-reproduction, and so, since "life" is merely a general 
term to denote the properties of self-reproducing matter, is pointing 
the way to the discovery of the nature of life itself. 

Before turning to discuss evolution, I will attempt to sum up as 
briefly as possible our present views on the mechanism of heredity. 

Heredity always has a physical basis. In every organism, plant or ani- 
mal, the genetic mechanism consists of a number of genetically sepa- 
rable unit-particles, the genes, arranged in a definite order along the 
visible cell-organs called chromosomes. For some part of the life his- 
tory in all organisms, and for almost all of it in all higher plants and 
animals, there are two complete sets of chromosomes and genes in 
every cell, one derived from the mother, the other from the father. 
(In some cases, the cells of certain tissues double or quadruple the 
number of their chromosome-sets.) The number of different kinds 
of genes is very large at least several hundreds even in bacteria, and 
up to several thousands or possibly tens of thousands in higher ani- 
mals such as flies or men. Each kind of gene can exist in a number 
of slightly differing forms called alleles, which produce different 
effects. Thus in rabbits, three alleles of one gene determine different 
color-types total albinism, partial albinism of the "Himalayan" type, 
white with black points, and full color respectively. The different 
alleles must have arisen by the mutation of one original gene. 

The number of different kinds of chromosomes in a set is much 



268 What Is Science? 

lower from one to rather over a hundred. The way in which the 
chromosomes behave in cell-division (mitosis), in preparation for sex- 
ual union (meiosis), and in sexual union (fertilization) determines 
the way in which genes are inherited and results in the genetic "laws" 
of segregation (Menders First Law), free assortment (Mendel's Sec- 
ond Law), and linkage. Segregation is what happens to pairs of al- 
leles lodged in the same chromosome. Thus, in Mendel's classical 
experiments, a tall strain of peas, carrying a pair of alleles for tallness 
(T T) were crossed with a dwarf strain (tt). The offspring all con- 
tained one T and one t allele, but all appeared tall, since T is dom- 
inant in its effects. But in meiosis, T and t segregated so that the 
gametes were all either T or t in equal numbers. Since fertilization 
is at random, the next generation consisted of 25 per cent TT, 50 
per cent Tt, and 25 per cent tt plants. The tt plants were again 
dwarfs and had segregated out pure from their hybrid parents. 

Free assortment describes what happens to two (or more) allele- 
pairs all lodged in different chromosomes. Each pair segregates inde- 
pendently of the rest, so that new recombinations of genes and char- 
acters are produced. Thus in the second generation from a cross 
between tall green-seeded and dwarf yellow-seeded peas, Mendel ob- 
tained tall yellow-seeded and dwarf green-seeded plants in addition 
to the parental types. 

Linkage is what happens to two or more genes which are lodged in 
the same chromosome. Their segregation is not independent, for the 
closer two genes are on the chromosomes, the more likely are they to 
segregate together, the less likely to become separated at meiosis, or 
to "cross over" as it is technically called. It is by ascertaining the cross- 
over percentages of different genes that geneticists can map their rela- 
tive position in a chromosome. 

Such a mechanism, it can be seen, has a number of important 
biological functions, and its operation explains many apparently un- 
related and puzzling phenomena. The fact that it is composed of self- 
reproducing matter provides for constancy of constitution and char- 
acter in time, even in face of great diversity of environmental 
conditions. The further fact that it consists of a large number of sep- 
arable self-reproducing particles or genes accounts for the familiar but 
at first sight surprising observation that members of a single family 



Evolution and Genetics 269 

may differ strikingly in their inherited characteristics. This is of course 
a consequence of the independent segregation of genes in sexual re- 
production, which results in the recombination of any mutants (ge- 
netic variations) present in the population. 

Mutation in its turn arises from the fact that the self-copying proc- 
ess is not always exact: inexact copying, where the inexactitude is 
spontaneous or caused by cosmic rays or other external agencies, 
results in the production of a self-reproducing mutant gene. There 
are thus two kinds of genetic variation, the first due to new mutation, 
the second to recombination, which may produce new combinations 
of existing mutants. Between them, these two sources of genetic varia- 
tion provide the raw material for evolutionary change. 

The further fact that most mutants are recessive to their normal or 
wild-type partners allows a species to build up a reserve of potential 
variability while preserving an effective constancy of character. This 
reserve variability may be of very different extent. Sexual reproduc- 
tion with regular outcrossing increases it; but both inbreeding and 
the dropping of sexual reproduction, as in parthenogenesis or apomixis 
or asexual (vegetative) reproduction, decreases and may totally 
abolish it. 

Sex itself is illuminated by our genetical knowledge. In origin it 
has nothing to do with sexual differentiation, the difference between 
males and females of a species; its basic and universal function is to 
provide the species with greater genetic variability. Neither segrega- 
tion nor recombination can occur in nonsexual reproduction. Sex 
brings together alleles from different strains. It thus increases variabil- 
ity and evolutionary plasticity, by combining mutants which would 
otherwise remain imprisoned in the separate lines in which they first 
arose. Sex thus permits the formation of a common pool of variability 
for the whole species. 

Finally, it enables us to understand many of the facts about species. 
For Darwin, the great problem was the origin of new species from 
old; once this had been accepted as a fact, the further problem pre- 
sented itself of how species attain and maintain their specific dis- 
tinctiveness. 

We can now say definitely that not only differences between spe- 
cies, but also those between genera and higher taxonomic categories, 



270 What Is Science? 

arise in the same way as differences between subspecies and minor 
intraspecific varieties. All spring from the same sources of variation 
mutations of various kinds and their recombinations and are 
brought about by the same mechanisms natural selection com- 
bined with some degree of isolation. The only difference is a quanti- 
tative one: more mutations and a longer span of time are required 
to bring about the greater amounts of difference. 6 

The second question, of how related species maintain their dis- 
tinctiveness and remain separate biological entities even when they 
inhabit the same area, can also now be answered. They remain dis- 
tinct because of some incompatibility to effective interbreeding. 
Sometimes the incompatibility depends on differences in behavior: 
the female of one species will not mate with the males of another. 
Sometimes it depends on timing: the flowering or spawning of 
related species of plants or aquatic animals takes place at different 
times of year. Often it depends on some incompatibility in the genetic 
mechanisms: the two gene-complexes are incapable of co-operating 
in development; or if they can so co-operate, as in the mule, they can- 
not co-operate in the maneuvers of meiosis, so that no functional 
gametes are produced; or if functional gametes are produced, many 
of the offspring resulting from fertilization are nonviable, defective, or 
sterile. To put the matter in a nutshell, if the differences between a 
new species and its relatives come to be too great in any aspect of 
reproduction, incompatibility follows. 

This is so in the great majority of animals; but in a few animals 
(e.g., some fish) and a considerable number of plants, quite distinct 
species, if brought together, will intercross and can still produce fer- 
tile offspring. This only occurs with species which normally inhabit 
different regions; whenever two closely allied species overlap geo- 
graphically, they possess some barrier to effective interbreeding, and 
this has undoubtedly often been strengthened by selection, in order 
to prevent the biological waste involved in intercrossing. 

To sum up, the essential achievement of the science of genetics has 

' Goldschmidt (1940 and later writings) still maintains that the large differences 
involved in what he calls macroevolution require a different type of mutation, a 
"macromutation" of large extent and radical effect, as against the ordinary muta- 
tions involved in small-scale "microevolution"; but he is now virtually alone in 
this contention. 



Evolution and Genetics 271 

been the discovery of the universal mechanism of inheritance. This is 
the gene-complex. It consists of hundreds or thousands of genetically 
separable units, the genes, but these interact and co-operate in de- 
velopment so that the gene-complex functions as a highly organized 
and integrated whole. The genes are lodged in orderly arrangement 
in the chromosomes, which provide the machinery for transmitting 
the gene-complex with quantitative accuracy, and for ensuring the 
recombination of different alleles in sexual reproduction. 

Finally, the occurrence of occasional mutation provides the herita- 
ble variation that gives species their reserve variability and consti- 
tutes the raw material of evolutionary change. 

When we come to evolution, including the past origin and future 
fate of existing animals and plants, we are confronted by an array of 
myths, superstitions and errors equal to those concerning heredity. 

The commonest myth is probably that of creation the idea that 
all organisms, including man, were created in their existing forms out 
of nothing, or out of raw materials like earth and water, by a god, at 
some definite moment in time. This is the myth found in Genesis, but 
variations of it occur in the mythology of many tribes and peoples. 

An opposed but equally erroneous myth is found in some eastern 
religions the idea of an endless cycle of recurrence, accompanied by 
transmigration of souls into different kinds of animals, by way of 
justice punishment or recompense as the case may be for the ac- 
tions of the soul in its previous existence. 

Often the idea of creation at a given date in the past was applied 
only to higher animals and plants, while lower forms were supposed to 
be spontaneously generated here and now. 

Coming to the early nineteenth century, when the idea of evo- 
lutionary transformation as opposed to once-and-for-all creation be- 
gan to be seriously entertained, we find Lamarck indulging in the er- 
roneous (but still persistent) belief that there was but a single ladder 
of nature or trend of advance from lower to higher, and in the super- 
stition of the inheritance of acquired characters. In spite of Darwin's 
demonstration of natural selection as a natural and inevitable mech- 
anism, by which evolutionary change could be brought about, many 
wishful thinkers preferred, like Samuel Butler, to rely on the Lamarck- 



272 What Is Science? 

ian idea of the inheritance of the results of will and effort; or, like 
Michurin and Lysenko, on the neo-Lamarckian idea of the inheri- 
tance of environmental effects; or, like Bergson and Bernard Shaw, 
on a mystical or vitalistic elan vital or Life Force; or, like some 
paleontologists, on the almost equally mysterious inherent trends that 
were supposed to produce "orthogenesis" or predetermined straight- 
line evolution in a given direction. 

The scientific study of evolution did not begin until after Darwin's 
publication of the Origin of Species in 1859. There were two reasons 
for this. First, Darwin presented an enormous mass of evidence which 
made it clear that transformation must have occurred. And secondly, 
he proposed for the first time a mechanism by which it could have oc- 
curred, in the shape of natural selection. It was of this key-concept that 
T. H. Huxley wrote ''My first reflection, when I first made myself 
master of the central idea of the Origin, was 'How extremely stupid 
not to have thought of that!' " 

Darwin himself extended the idea of evolution to include the ori- 
gin of man from apelike ancestors (1871) and the evolution of mind 
and behavior as well as of bodily structure and physiology (1872). 
Meanwhile an immense amount of attention was devoted to the study 
of individual evolution or development, which we call embryology or 
ontogeny; and remarkable paleontological discoveries began to be 
made, confirming in the most striking way Darwin's deductions that 
the evolutionary advance of a group of animals and plants is brought 
about by its radiation into a number of separate lines or lineages, in 
each of which transformation is gradual and tends toward the im- 
provement of the lineage for a particular way of life. 

The concept of evolution was soon extended into other than bio- 
logical fields. Inorganic subjects such as the life-histories of stars and 
the formation of the chemical elements on the one hand, and on the 
other hand human subjects like linguistics, social anthropology, and 
comparative law and religion, began to be studied from an evolution- 
ary angle, until today we are enabled to see evolution as a universal 
and all-pervading process. 

But before discussing evolution in this extended sense, I must men- 
tion a few more milestones in the study of biological evolution. Dur- 
ing the latter half of the nineteenth century, the comparative study of 



Evolution and Genetics 273 

morphology, embryology, geographical distribution and paleon- 
tology, had provided a broad picture of the relationships and proba- 
ble evolution of the main groups of animals; while the intensive work 
of the great naturalists had brought to light the range and complexity 
of the detailed adaptations achieved by natural selection. Further- 
more, fossil hominids more apelike than modern man had been dis- 
covered, together with a remarkable sequence of his and their stone 
implements; and in the present century a series of further finds have 
now bridged the gap between Homo sapiens and the anthropoid apes, 
or at least provided an adequate set of steppingstones. 

In 1900, the event occurred which was destined to exert the greatest 
influence on evolutionary theory since Darwin's day the rediscov- 
ery of Mendel's work, which soon led to the conclusion that the in- 
heritance of mendelian characters must be particulate, dependent on 
a set of material unit-particles transmitted from parents to offspring. 
By about 1915, it was becoming clear that almost all inheritance was 
particulate, that the particles involved were the genes arranged along 
the chromosomes, and that the raw material of evolutionary change 
consists of the mutations or self-perpetuating variations which from 
time to time occur in the hereditary material. At first, for the simple 
reason that the earlier geneticists had naturally preferred to work with 
pairs of characters showing large and striking differences, the facts of 
Mendelism did not seem to fit in with Darwin's belief in continuous 
gradual evolutionary transformation, but rather with de Vries' idea of 
sudden large jumps or quanta of change. However, it was soon dis- 
covered that the great majority of mutations actually utilized by or- 
ganisms are of small extent, and that frequently a number of genes 
with small effects combine to form the genetic basis of a given char- 
acter. And this idea of the functional interrelation of genes was later 
generalized, until, as already mentioned, the idea of the gene- 
complex was born the realization that the hereditary constitution is 
not a set of separate gene-units, each exerting its effect in isolation 
from its fellows, but a highly organized whole, whose parts operate in 
closely adjusted interrelation with each other, so that for instance a 
particular gene transferred to the new genie environment provided 
by a different gene-complex, may and usually does produce quite dif- 
ferent effects on the visible characters of the organism. 



274 What Is Science? 

It speedily became clear that selection acting on gene-complexes 
of this type could produce apparently continuous transformation of 
animals and plants in their evolution. And finally, in 1930, R. A. 
Fisher laid the foundations of modern evolution theory with his no- 
table book The Genetical Basis of Natural Selection. In this, he not 
only demonstrated mathematically how selection acting on small mu- 
tations of the extent and frequency known to occur in nature, could 
produce gradual and continuous transformation, but also proved that 
evolutionary transformation could not take place on the basis of the 
"blending inheritance" postulated by Darwin and most of the bio- 
metricians, but required a participate mechanism. 

Fisher further demonstrated the theoretical impossibility of La- 
marckism involving the inheritance of acquired characters, or of ortho- 
genesis involving an inherent urge or will or tendency to evolve in 
a particular way, playing or having played any significant part in bring- 
ing about evolutionary change. 

Such theoretical demonstrations of impossibility may be of great 
importance for the development of science for instance the impos- 
sibility of constructing a perpetual motion machine; the impossibil- 
ity of heterogenesis, or the production of one kind of animal by a 
quite different kind; the impossibility, according to Einstein's special 
theory of relativity, of bodies moving with a velocity faster than light; 
or the impossibility of alchemy in the traditional sense. 

Fisher's demonstration of the impossibility of Lamarckism and or- 
thogenesis acting as agents of evolutionary change means that we need 
waste no more time and energy on these subjects, but can concen- 
trate on the study of natural selection. Thanks to the work of Fisher, 
ably extended by men like Haldane and Sewall Wright, we can now 
confidently say that natural selection is overwhelmingly the main 
agency of evolutionary change, and the only agency of evolutionary 
direction. 7 

7 When a few individuals are isolated, say on an island, they are not likely to con- 
tain all the alleles possessed by the species as a whole. Further, in very small popu- 
lations, alleles may occasionally be lost from the gene-complex, resulting in what 
Sewall Wright calls "drift." The resultant changes in character of the population 
will be random, not directional or adaptively related to the environment. But 
those nonadaptive statistical accidents play only a very small part in the evolution- 
ary process. 



Evolution and Genetics 275 

Natural Selection is the phrase used by Darwin to denote what 
might more accurately be called the differential survival of variants in 
relation to the conditions of life. 

Given the basic facts of life self-reproduction and mutation this 
follows as an inevitable consequence. For instance, if a mutation 
gives rise to a mutant which has an average chance of survival only 
one-half of one per cent higher than the allele from which it arose 
that is today, if on the average 200 of the mutants survive and re- 
produce themselves in each generation as against 199 of the original 
then in a biologically short period, it will replace the original form 
as the normal type of the population. Natural selection thus works not 
by all-or-nothing elimination, involving 100 per cent death as against 
100 per cent survival, but by slight average extra survival over a num- 
ber of generations; further, it may be concerned with all kinds of 
characteristics, from ability to escape detection to speed in pursuit, 
from passive armor-plating to greater intelligence, from extra viability 
or biological "toughness" to higher fertility or success in mating. 

For reasonably rapid evolutionary change to take place, it is clearly 
necessary that favorable mutations occurring in separate stocks or 
lines should be capable of being brought together and combined in 
a single line; this is of course achieved by means of sexual recombina- 
tion. 

The picture becomes more complex when we find that mutants 
which are unfavorable when acting alone may sometimes be favor- 
able when combined, or that a mutant which is selected against in one 
set of circumstances, is favored when conditions change (as happened 
with the black mutants of many moths in areas which became in- 
dustrialized). 8 It is for such reasons that the reserve store of recessive 
mutant gene found in all outcrossing species is so important; it 
provides a reservoir of potential variability which can be drawn 
upon as the occasion demands. 

In Fisher's epigrammatic phrase, natural selection is a mechanism 

8 A considerable number of species of moths in Britain and western Europe have 
become melanic (black or nearly so) in industrialized areas during the past 100 
years. This was due to the fact that the melanics survive better than the normals 
in unfavorable conditions, such as for instance the contamination of their food- 
plants with smoke. The normals have the advantage of being protectively colored, 
and in rural conditions this outweighs the extra hardiness of the melanics. 



276 What Is Science? 

for generating an extreme degree of (apparent) improbability 
improbability of such a high order that it could never have been pro- 
duced by chance alone without the aid of natural selection, any more 
than monkeys tapping on typewriters could ever produce a play of 
Shakespeare. Given the facts of life and the known extent of bio- 
logical time, such apparently improbable results as the protective re- 
semblance of a Kallima butterfly to a dead leaf, or the evolution of 
organs of stereoscopic color vision like our own eyes, become com- 
prehensible and scientifically explicable. 

The study of how selection acts on the organisms in different cir- 
cumstances led, among other things, to the realization that their gene- 
complexes evolve adaptively just as much as do their bodies and their 
behavior; and much study, largely initiated by Darlington, was de- 
voted to the problem of the evolutionary effects to be expected from 
gene-complexes of different types. 

In particular, it became clear that the retention of a genetic system 
promoting outbreeding will favor variability and therefore evolution- 
ary flexibility in the face of any change in environmental conditions. 
On the other hand, the change-over to one of the many systems pro- 
moting inbreeding or rendering outcrossing difficult or impossible, 
will increase immediate fitness in the sense of close adaptation to the 
existing environment, but is likely to lead to failure and probable 
extinction in the evolutionary long run. 

Meanwhile the notable discovery by Muller in 1927 that genes 
could be artificially induced to mutate by means of X-rays, at a rate 
many times higher than that of natural mutation, led to a huge crop 
of new research. Among other notable results, it was found that 
chromosome-doubling (polyploidy) could be produced by means of 
the chemical substance colchicine, thus giving rise to many plants 
and some animals with four instead of the normal two complete sets 
of chromosomes; and this has enabled plant breeders to make many 
otherwise impossible fertile crosses between species with different 
numbers of chromosome-sets, and so to initiate various new lines of 
artificially directed evolution. (A hybrid between species with four 
and two chromosome-sets has three chromosome-sets and is sterile. 
For a fertile cross, the two parents must have the same number of 
chromosome-sets.) More importantly, it was discovered that many 



Evolution and Genetics 277 

other agencies besides X-rays, some of them physical like ultraviolet 
radiation, others chemical like mustard gas, are capable of inducing 
mutations, and that certain of these mutations appear to be caused 
only by certain agencies. This discovery was later turned to practical 
account, notably in the production of strains of the mold Penicil- 
Hum giving much higher yields of penicillin than those found in na- 
ture. 

Of late years, a great deal of research has been carried out on uni- 
cellular microorganisms, including bacteria. This has had two main re- 
sults of importance. First, it has enabled us to discover in many cases 
how genes act and what they do, because in microorganisms there is 
normally no long and complex process of development, and a gene 
is often directly concerned with the production of some chemical sub- 
stance required in the cell's basic metabolism. And secondly, repro- 
duction is so rapid that it has permitted us to study in the space of a 
few weeks or months, evolutionary effects of mutation and selection 
which in higher organisms would require decades or even centuries. 

Then, during the last two decades, the viruses, those strange en- 
tities which occupy a position intermediate between the living and 
the nonliving, have also received much attention. It has been discov- 
ered that these subcellular organizations (it is better not to beg the 
question by calling them organisms), even when capable of being 
crystallized in pure chemical form, exhibit the basic phenomena of 
genetics they are composed of a number of separable self-copying 
units analogous to genes; they exhibit genetic variation analogous to 
that produced by gene-mutation; and in some cases when two differ- 
ent varieties are mixed, the offspring exhibit a recombination of char- 
acters analogous to that produced by the sexual process. 

In the very different but equally important field of paleontology, 
the present half-century has seen great activity, notably in the un- 
earthing and analysis of trends or lineages of fossil animal groups, thus 
giving us for the first time a reasonably accurate and detailed picture 
of the actual course of evolution in different groups in various cir- 
cumstances and in various periods of the earth's history. 

Finally, there has been in the last fifteen or twenty years a remark- 
able movement toward a synthesis of the various disciplines relating 
to biological evolution. This has been undertaken by paleontologists 



278 What Is Science? 

like George Gaylord Simpson, by taxonomists like Ernst Mayr, by 
geneticists like Theodore Dobzhansky, and by general biologists like 
myself, and has been promoted by the founding of special journals 
devoted to the subject, like Evolution, so that we are now witnessing 
the rapid growth of a unified science of evolutionary biology. 

Furthermore, with the adoption of the evolutionary approach in 
nonbiological fields, from cosmology to human affairs, we are begin- 
ning to realize that biological evolution is only one aspect of evolu- 
tion in general. Evolution in the extended sense can be defined as 
a directional and essentially irreversible process occurring in time, 
which in its course gives rise to an increase of variety and an increas- 
ingly high level of organization in its products. Our present knowledge 
indeed forces us to the view that the whole of reality is evolution a 
single process of self-transformation. 

Further analysis speedily reveals that this universal evolutionary 
process is divisible with three main sectors or phases the inorganic 
or cosmological, the organic or biological, and the human or psycho- 
social. Each sector has its own characteristic mechanism of self- 
transformation and its own maximum rate of change, and each pro- 
duces its own characteristic type of results. 

The inorganic sector is almost infinitely the largest in spatial extent 
and in mass, as it comprises the entire universe of galaxies and inter- 
galactic space, with the exception of the few small areas where living 
matter has developed. The methods of change operating in it are 
very simple, being confined to physical and occasional inorganic 
chemical interactions. The resultant processes of transformation are 
in general extremely slow, so that the life-history of a star is to be 
measured in thousands of millions of years. Finally, the resultant 
products never attain to any but very low or simple levels of or- 
ganization. At the submicroscopic end of the scale, matter in the 
cosmological sector exists for the most part on the atomic or sub- 
atomic level, though it occasionally comes to be organized in the form 
of molecules or of simple chemical compounds; while on the grand 
scale, the complexity of organization goes no further than the sim- 
ple spiral pattern of the galaxies, and the concentric structure of the 
stars. 

In correlation with this, the inorganic sector has given rise only to a 



Evolution and Genetics 279 

very limited variety of products on the one hand the various types of 
subatomic particles, the different chemical elements, and a quite small 
range of chemical compounds; and on the other hand, the few kinds 
of stars, together with their occasional appendages such as comets and 
planets, and the still fewer kinds of galaxies or spiral nebulae. 

In the biological phase 9 the time-scale is still very extensive, though 
somewhat less so than that of the cosmological phase nearly 2000 
million years since the first appearance of life on earth as against 
about 5000 million years or somewhat less for the age of our own 
galaxy. 

The amount and rate of change produced, however, is immensely 
greater. If we think first of variety, we find that biological evolution 
has produced organisms as diverse as starfish and roses, men and toad- 
stools, tapeworms and oak trees, birds and bacteria, with an amaz- 
ing range in size, in method of working, and in organization and plan 
of construction. There are now in existence about a million and a 
half distinct and separate species of animals and plants, all of them 
presumably derived from one original form. 

Equally amazing is the degree of detailed adaptation achieved. We 
need only think of the wings of a hover-fly, the eyes of a falcon, the 
luminous lures of deep-sea angler-fish, or the mechanisms of orchids 
for securing cross-pollination by insects. 

Most remarkable of all, however, is the rise in level of organization. 
The earliest organisms must have been submicroscopic units, of 
the same order of complexity as modern viruses; and for tens or hun- 
dreds of millions of years life did not rise above the unicellular level. 
In contrast with this, we find that later evolution has produced or- 
ganizations of such almost miraculous elaboration as the flying birds, 
the gigantic plankton-feeding whales, the temperature-regulating 
mechanism of higher mammals, the societies of ants and bees, and 
the human cerebral cortex the most complex system of which we 
have any knowledge. 

This vast increase in the tempo and amount of change has been 

* I am restricting myself to the biological phase on this planet, since here only do 
we have any firm knowledge of it. There is, however, the scientific probability that 
life (complex self-reproducing and self -varying matter) has been produced on a 
number (several hundreds or even thousands) of other planets in our galaxy. 



280 What 1$ Science? 

made possible, as I have already indicated, by the availability of 
a new method of self-transformation natural selection. 

The actual course taken by biological evolution has now been re- 
vealed in detail by fossil evidence in a number of groups such as 
horses, trilobites, elephants, ammonites, and various types of dino- 
saur; and with reasonable accuracy in a larger number, such as most 
other mammalian orders, including the primates with man himself, 
and many groups of fish and reptiles; while it can be deduced in 
broad outline in many other types, both plant and animal. 

We find the following general results. First, each new group pro- 
ceeds to break up or diverge into a number of different lines, each of 
which becomes increasingly specialized, or improved for a par- 
ticular mode of life. This process of divergent specialization operates 
at various levels. Thus the higher or placental mammals have diverged 
into a number of Orders the carnivores for active catching of large 
prey, the insectivores for small prey, the bats for flying, the rodents for 
gnawing, the ungulates as herbivores, the primates for tree life, the 
whales and porpoises for a fully aquatic existence. Each of these in 
turn has diverged into a number of finer specializations the carni- 
vores, for instance, into seals, sea-lions, cats, dogs, weasels, bears, etc., 
and these smaller groups have repeated the process, which ends up 
with the formation of separate species each adapted to its own special 
niche: thus the cats have produced the lion, the tiger, the lynx, the 
bobcat, the fishing cat, the puma, the leopard, the jaguar, the ocelot 
and various other feline species. 

In the great majority of cases this process of divergent specializa- 
tion sooner or later comes to an end: the type becomes stabilized at a 
certain level, and after that remains constant in essentials, though still 
often capable of minor alterations on that level, alterations which are 
merely variations on an existing theme, and do not radically change 
it or introduce a new theme. The classical example is that of the 
horse family, the Equidae. This, after nearly 50 million years of 
gradual and steady specialization or improvement of limbs for speed 
and of teeth for chewing vegetable food, 10 became stabilized in its 

10 In the latter half of this period, the more successful branch of the family special- 
ized for running on open plains, and for chewing hard flinty-stemmed plains grasses 
rather than woodland leaves. 



Evolution and Genetics 281 

definite form around five million years ago; and since then has 
merely rung the changes on this form by evolving into the various 
species of zebra, true horse, and wild ass. 

As T. H. Huxley pointed out three-quarters of a century ago, nat- 
ural selection is the only agency capable of producing change or the 
absence of change according to circumstances. But before discussing 
this point further, I must deal with the subject of so-called dominant 
groups. 

In the actual course of evolution as revealed by fossils, we find a 
succession of these dominant groups, each of them arising at a certain 
period of evolutionary time, rapidly becoming more successful and 
abundant through divergent specialization, and finally becoming sta- 
bilized in all or almost all of its branches. Meanwhile the previously 
dominant group, from among whose more primitive members the 
new successful group has originated, is much reduced in numbers and 
in variety, many (and sometimes all) of its branches becoming ex- 
tinct. 

The classical example is that of the land vertebrates. Before the De- 
vonian, a little over 300,000,000 years ago, there were no land verte- 
brates: all the backboned animals in existence were fish (or of 
more primitive fishlike types). In the Devonian, the amphibians ef- 
fected a partial colonization of the land. 

After the comparatively short period of some 70 million years, the 
reptiles rose to dominance, in virtue of the improvements in bodily 
organization and reproduction (dry scaly skin and large-yolked shelled 
egg) which permitted their full conquest of the land. The amphibians 
declined in importance, but the reptiles blossomed out into a fan- 
tastic array of specialized types dinosaurs, crocodiles, plesiosaurs and 
ichthyosaurs, tortoises, pterodactyls, and many others. 

However, at the close of the Mesozoic, after over 1 50 million years 
of reptilian supremacy, the two new groups of the birds and the mam- 
mals rose to joint dominance on land, in virtue of their new capacity 
for keeping themselves at a constant high temperature, their much 
greater parental care of their young, and, especially in the higher mam- 
mals, their improved brains. The majority of reptilian types became 
extinct, and during the Cenozoic the birds and mammals radiated 
out into an exuberance of specialized lines. After about 60 million 



282 What Is Science? 

years this phase was brought to an end by the Ice Age, and by the 
rise of the latest dominant type in evolution, Man. As before, with 
the rapid expansion of the new type was correlated widespread reduc- 
tion and extinction of the previously dominant types, especially the 
mammals. We need only think of the fate of mammoths, sabertooths, 
giant sloths and giant wombats, or more recently, of aurochs and 
quagga, passenger pigeon and great auk. 

Essentially similar successions of dominant types are found in aqua- 
tic vertebrates, in aquatic arthropods, in mollusks, and in insects. 

Two general points need stressing. First, each new dominant type 
owes its dominance not to any specialized adaptation but to some 
new mechanism of importance in general biological organization. 
And secondly, stabilization after rapid improvement and expansion 
is the fate of most dominant types as of specialized lines. Thus the 
reptilian type seems to have exhausted all its possibilities of major 
advance during the Cretaceous, though considerable changes were 
still possible within the reptilian level of organization (e.g., those lead- 
ing to the evolution of snakes). And the birds have not shown any 
improvement qua flying machines for at least 20 or 30 million years, 
though they have been improved for a diversity of habitats and ways 
of life. 

Even ants, which are in many ways the highest type of inverte- 
brates, became stabilized over 35 million years ago; the ants which 
we find beautifully preserved in Baltic amber are specifically but not 
even generically distinct from those alive today. 

Thus the great majority of animal and plant groups, large and small 
alike, are restricted in their evolutionary possibilities. After a longer 
or shorter time, they become stabilized at a certain maximum level of 
biological organization. On this level, they may continue to evolve, 
producing new variations on their basic organizational theme. These 
variations may be quite considerable, as in the previously mentioned 
case of the evolution of the snakes, whose construction opened up 
new ways of life to its possessors. But this, though an important nov- 
elty, was achieved on a purely reptilian level: the snakes show no im- 
provements in basic organization such as characterized either birds or 
mammals. 



Evolution and Genetics 283 

Very occasionally, such basic advances and improvements are 
achieved; and they then make possible the rise of a new dominant 
group on a new level of biological organization. Evolutionary progress 
takes place by a series of such steps from lower to higher levels of 
organization. 

Restriction of evolutionary possibilities may be due to a number 
of rather different causes. In the first place, specialization for a par- 
ticular way of life leads to a cul-de-sac. This is partly because the 
mechanisms concerned eventually reach a state at which further 
change in the same direction would be disadvantageous; thus in the 
horses, further elaboration of the grinding pattern of the molars 
would produce a "millstone" too finely patterned for efficient grind- 
ing of the grass-stems on which they feed, and the reduction in the 
number of their digits can obviously not go below one! Furthermore, 
the specialized type soon becomes so well-adapted to one mode of 
life that it cannot change to another: too many mutations would be 
simultaneously required to enable it to climb out of its old evolu- 
tionary groove into a new one. 

Improvements in general efficiency or organization also tend to a 
limit. Thus it would apparently be of no biological advantage for a 
bird or a mammal to evolve a greater accuracy in regulating its tem- 
perature; and the fact that the units of vision in a vertebrate are sin- 
gle cells, and therefore must be above a certain diameter, makes it 
impossible to construct an eye with an acuity of vision greater than 
that of a falcon. 11 

Sometimes the restriction is indirect. Thus the breathing mecha- 
nism of insects, by means of minute tubes or tracheae taking air di- 
rect to the tissues, while very efficient at small sizes, rapidly becomes 
less efficient with increasing bulk, with the result that an insect the 
size of a rat could not function at all, and in fact none exist larger 
than a mouse. This limitation of total size in turn limits the size of 
the brain and the number of nerve-cells in it; and this again limits 
learning capacity and mental plasticity. Thus the adoption of the tra- 

11 In the compound eyes of insects, the units of vision, the omiuatidia, have a larger 
minimum size, which restricts the acuity of vision and resolving power to a con- 
siderably lower level. 



284 What Is Science? 

cheal system of respiration by insects restricted their possibilities of 
intelligence, and therefore of their competing with man for the posi- 
tion of new dominant type. 

When we survey the biological panorama as a whole, we see that 
evolution is from one point of view the realization of the possibil- 
ities of living substance: evolutionary advance and progress involve 
the successive realization of new possibilities. Further, we are driven 
to the rather surprising conclusion that some time during the late 
Cenozoic, probably about five million years ago, all the purely ma- 
terial or physiological possibilities of life had been actualized and 
had reached the upper limit of realization. Though it is difficult to 
prove such a universal negative, it certainly holds good, as already 
mentioned, for visual acuity and accuracy of temperature regulation, 
and also for many other features, such as size in land animals, speed 
of locomotion, elaboration of instincts, digestive and mechanical ef- 
ficiency, and protective resemblance; and its general applicability is 
rendered probable by the fact that the evolutionary level of all 
major groups of animals seems to have become stabilized by this 
period. 

One major avenue of advance, however, remained the further 
realization of mental possibilities. It was this direction which was 
taken by our earliest hominid ancestors and led to the emergence of 
our own species as the latest dominant type of evolution. 

With the advent of man, evolution on this planet enters the human 
or psychosocial phase. Man's distinctive property of conceptual 
thought, with its objective correlate in the shape of true speech, 12 as- 
sured him his position of biological dominance by providing him 
with a totally new method of evolutionary change the method of 
the cumulative transmission of experience. 

By means of spoken and still more effectively of written language, 
man can do what is possible to no other organism, namely transmit 
the results of experience to later generations and do so cumulatively. 
This constitutes a second mechanism of inheritance, in addition to 

"By true speech I mean a method of communication which employs arbitrary 
symbols (words) to denote things or ideas, instead of one which, like all others 
employed by animals, uses innately-determined sounds or gestures to signify emo- 
tional or behavioral states. 



Evolution and Genetics 285 

that of biological genetics. What this exclusively human mechanism 
transmits is not a system of material units as in biological inheritance, 
but a system of knowledge, ideas and attitudes. We may sum up the 
essential difference between the three sectors of evolution by saying 
that whereas evolution in the biological sector depends on its new 
property of the self-reproduction of matter, in psychosocial evolution 
it depends on the self-reproduction of mind. 

The result is that in the psychosocial sector evolution is prepon- 
derantly cultural, not genetic. While the intrinsic genetic character of 
man, mental as well as bodily, has not changed appreciably since the 
end of the Paleolithic, those of his societies and cultures have done so. 
What is more, this cultural evolution has proceeded at an unprec- 
edented rate, many hundred times greater than even the fastest 
changes found in biological evolution; for the new mechanism of 
transmission of experience immensely speeds up the processes of 
change. Furthermore, because the transmission of experience is cu- 
mulative, the rate of change can show an acceleration instead of a 
steady maximum, and this is precisely what we find: it is common 
knowledge that the rate of change in human affairs has risen since be- 
fore the dawn of history, and is now proceeding at an almost ex- 
plosive speed, a speed at which major changes in ideas and material 
conditions often succeed each other faster than do human genera- 
tions something unprecedented in previous centuries. 

This acceleration of cultural evolution obviously depends on two 
main factors improvements in the methods of acquiring new experi- 
ence, and improvements in the mechanism of transmission of ex- 
perience once acquired. The invention of writing and later of print- 
ing are examples of the second, while the use of the scientific method 
and its application to an ever-widening range of subjects are exam- 
ples of the first. 

As a result of this high and accelerating rate of change, we find that 
in the less than 10,000 years since the discovery of agriculture, psycho- 
social evolution has produced a degree of variety and a rise in organiza- 
tional level comparable with those achieved by biological evolution 
in the last 1,000,000,000 years a period a hundred thousand times 
greater. 

Innumerable examples of human variety come to mind once one 



286 What Is Science? 

begins to think of the different types of society, the artistic and sci- 
entific achievements of different cultures and individuals, the differ- 
ent religions and ideologies, that have come into being since the be- 
ginning of the Neolithic. During the same period, the highest level of 
organization has risen through the following main steps. First, food- 
gathering and hunting tribes; then agricultural village communities; 
small urban communities; early civilizations with cities, the use of 
metals and writing, with widespread commercial transport organiza- 
tions, and with the dawn of systems of organized scientific and tech- 
nological knowledge; later civilizations, with moderate technological 
advance, including printing and ocean-going ships; early scientific civ- 
ilizations with restricted use and application of science (paleo- 
technic); and modern scientific civilizations with deliberate and ex- 
tended use and application of science (neotechnic). Finally, the last 
few decades have seen the first beginnings of organization on the 
world level. 

This is not the place to discuss the psychosocial phase of evolution 
in detail. But it is worth while pointing out a few of the ways in 
which it differs from the biological phase. First and foremost, as al- 
ready stressed, is its radically different method of self-transformation. 
This at once implies that we cannot apply the conclusions drawn 
from biological evolution directly to human affairs. Genetic change 
due to the automatic working of natural selection, for instance, is 
now only of subsidiary importance in the psychosocial sector. How- 
ever, genetic change guided by conscious purpose could come to be 
extremely important: it is already clear theoretically that we could 
appreciably raise the average of desirable genetic qualities in man, such 
as health, vigor, intelligence, and various special aptitudes. Practically, 
however, this would require not merely more scientific knowledge, 
but a radically changed attitude to the problem. 

Meanwhile the facts of cultural diffusion and culture-contact make 
it evident that cultures and societies evolve in quite different ways 
from those available to the rigidly separate lines of biological evolu- 
tion. In human evolution, cultural elements can diffuse and interpene- 
trate other societies; the genetical elements of biological evolution are 
incapable of diffusing and interpenetrating other organisms. 

Another extremely important difference is this that whereas major 



Evolution and Genetics 287 

evolutionary advance in the biological sector appears to have reached 
its limit, the psychosocial sector is in an extremely early phase of its 
evolution, with enormous possibilities of change and advance still 
unrealized. The new dominant type constituted by man is in a very 
young stage of its evolution, corresponding more or less with that 
reached by the mammals in the early Eocene. 

A further radical difference is that whereas all dominant (and 
other) biological types rapidly diverge into a large number of separate 
lines orders, families, genera and species man has remained biolog- 
ically a single unit. The incipient divergence which gave rise to the 
major races or subspecies of Homo sapiens was early counteracted 
by a process of convergence, due to man's incurable restlessness, 
which has brought together representatives of different racial groups, 
and to his tolerance of diversity in mating; and this convergent inter- 
crossing, which has proceeded with an increasing rapidity in modern 
times, has kept mankind as a single species or interbreeding group. 

Cultural and ideological divergence proceeded much further in man 
than did genetic divergence, giving rise to a huge array of distinctive 
cultural "species": the vertical difference between ancient Assyrian 
and modern American culture is as important as that between an 
amphibian and a mammal, and the lateral difference between, say, 
Eskimo and Melanesian society is as great as that between a snail and 
a shrimp. But this too is now being counteracted by a process of con- 
vergence. Science is potentially universal, and its technological and 
medical applications are spreading rapidly all over the world. Psycho- 
social evolution is surely heading toward a single unitary pool of 
knowledge and ideas, and ideological convergence is clearly the goal 
to be aimed at. On the other hand, this ideological and scientific 
unity should equally clearly be combined with the maximum amount 
of cultural richness and diversity. 

Another distinctive character of man is the much greater impor- 
tance of the exceptional individual in cultural than in biological evo- 
lution. This is shown not only by the effects which exceptional in- 
dividuals like Napoleon or Genghis Khan or Lenin may exert on the 
course of history, but more importantly in science and the arts, where 
fundamental discoveries and enduring masterpieces are always the 
work of exceptional individuals. 



288 What Is Science? 

Population also constitutes a distinctive human problem. Not only 
have the total human population and its absolute annual increment 
increased more or less steadily since the end of the Paleolithic, but 
also its percentage (compound interest) rate of increase. Before the 
Neolithic, this must have been well below 0.1 per cent per annum; by 
the late seventeenth century, it had reached 0.25 per cent; and in 
the eighteenth century, 0.5 per cent. Within the last few decades it 
passed one per cent for the first time. It is now well above that figure 
and still going up. 

In animals, excessive population is regulated by death from famine, 
disease, or climatic extremes; man is unique in being able to regulate 
it consciously by infanticide or abortion, as in many primitive so- 
cieties, or by deliberate birth control. Probably the most important 
task now before man is to discover a simple and cheap contraceptive 
and to embark on a world policy of population control. 

Another grave modern problem, made more urgent by the inven- 
tion of the various types of atom bomb, is the prevention of war, 
coupled with the task of harnessing atomic energy for constructive 
purposes, while shielding the human germ-plasm from its deleterious 
effects. But this is an immediate, political problem in the forefront of 
public consciousness, and it would be out of place to discuss it in 
detail here. 

It is more important to set down some of the general implications 
of the evolutionary approach to human affairs. I would first of all re- 
mind my readers that evolution in the psychosocial sector human 
history in the broad sense is an extension of the general process of 
evolution, but that it operates with the aid of a quite new mechanism 
and produces quite new kinds of result. 

Evolution can be envisaged as a progressive realization of intrinsic 
possibilities. Man is the latest dominant type in biological evolution, 
and the first (and up till now the only) dominant type in psychosocial 
evolution. His destiny is to act as the agent of the evolutionary process 
on this planet, by enabling it to realize new and higher possibilities. 
This he can accomplish only if he utilizes to the fullest possible ex- 
tent the new mechanism of self-transformation which his ancestors 
achieved the employment of cumulative experience in the service of 
conscious purpose. Biological evolution, though it often displays di- 



Evolution and Genetics 289 

rection, is directed from behind, by the blind and automatic force 
of natural selection: psychosocial evolution can be, to a lesser or 
greater extent, directed from in front, by the anticipatory force of 
conscious purpose. Thus the long-range task of the human species is 
to establish a fully conscious common purpose, based to the fullest 
possible extent on scientifically established knowledge. 

If we hope to sum up the situation epigrammatically, we can say 
that, with the advent of man, conscious purpose was able for the first 
time to exert an operative effect on evolution; and that through the 
new knowledge acquired during the last hundred years, the evolu- 
tionary process was able for the first time to become conscious of it- 
self. The next decisive step in evolution will accordingly be the fuller 
development of that self-consciousness. In particular it will be the 
conscious clarification of the future in the light of the long evolution- 
ary past and of the study of human potentialities. Once this has been 
done, greater realization of possibilities rather than higher produc- 
tivity, fulfillment rather than efficiency, will become the overriding 
aim. 



PSYCHOLOGY 



EDWIN G. BORING 



about 

Edwin G. Boring 



Edwin G. Boring was born in Philadelphia, in 1886 and after iocal 
schooling went to Cornell to study electrical engineering. In 1908, 
having got his degree, he spent a year with the Bethlehem Steel 
Company finding out, as he says, that what he had wanted all along 
was physics or "some kind of science 1 ' and not engineering. There- 
upon he went back to Cornell for graduate work in physics but "got 
caught by psychology, perhaps because I was allowed with little train- 
ing to do a tiny bit of psychological research on learning in protozoa." 
His first job in the science he finally chose as lifework was a Cornell 
assistantship in psychology at $500; this supported him while he 
worked for his Ph.D., which was awarded in 1914. The day after he 
got his degree he was married his wife is also a psychologist, lie 
stayed on to teach at Cornell until Americas entry into the First 
World War when he was assigned by the Army to give intelligence 
tests to recruits at Camp Upton, Long Island. For a brief period after 
the war Boring held a professorship in psychology at Clark Univer- 
sity, but in 1922 he moved to Harvard where he soon became pro- 
fessor and director of the renowned Harvard Psychological Labora- 
tory, a post he held for twenty-five years (1924-1949). Boring says he 
went to Harvard determined "to get its psychology out of the clutches 
of its philosophers': in this aim he was successful, furthering it by 
his experimental work and by the publication of more than 200 arti- 
cles, some describing his researches (he remarks that his experiments 

292 



about Edwin G. Boring 293 

have done most to show "why the full moon looks large on the hori- 
zon"), some theoretical, some historical. His best known work is the 
History of Experimental Psychology, published in 1929 and revised in 
1950, a fascinating book which has done a great deal to make Ameri- 
can graduate students in psychology aware of the background of their 
specialty. He has also written a history of experimental work in the 
psychology of sensation and perception. He is a member of the Na- 
tional Academy of Sciences and former president of the American 
Psychological Association. 

Boring is 69, but has not retired. "I cannot decide," he says, 
"whether I would like to retire so as to have more time to do the 
things in psychology I am chafing to do or whether I want to keep 
closer contact with the Harvard Psychological Laboratories so that I 
can keep on being stimulated as I am now. I'd like to do both." Bor- 
ing is primarily an experimentalist, yet there is no branch of psychol- 
ogy alien to his understanding. He has the breadth of outlook and 
hospitality to ideas which mark the true scientist. 



PSYCHOLOGY 

EDWIN G. BORING 



On Tuesday morning, October 22, 1850, Gustav Theodor Fechner 
was lying in bed in his home in Leipzig, Germany, wondering what 
science could do to combat the growing materialism of the age. Fech- 
ner was a German scientist and scholar, a man of broad outlook, of 
substantial erudition and of patient and thorough habits of work. 
He had been a professor of physics at the university in Leipzig, but 
for ten years now he had been ill and incapacitated for work. Perhaps 
in part because of this illness and perhaps also in part because he 
was getting older he was forty-nine in 1850 his interest had become 
fixed on the nature of the spiritual, the nonmaterialistic world. 

It occurred to Fechner that morning this is one of those rare oc- 
casions when an important scientific insight can be dated almost to 
the exact hour of its occurrence it occurred to him that, if you could 
show how the spiritual and the material are related, you would be 
demonstrating that there is after all only one world and that the 
opposition between the two would then disappear. He recalled the 
experiments of E. H. Weber, the physiologist, sixteen years earlier. 
Weber had shown that the just noticeable difference between the 
intensities of two sensations between the brightnesses of two lights 
or the heavinesses of two weights occurs when the difference be- 
tween the intensities of their stimuli is a fixed proportion of the 
stimuli. If you can just barely distinguish the difference in weight 
between 29 and 30 ounces, Weber found, then you will also be 

294 



Psychology 295 

able just barely to distinguish the difference between 58 and 60 
ounces and also between 29 and 30 drams (1 dram^/s oz.). 

Such a fact was just what Fechner needed. Here he had an ob- 
servable relation between spiritual events (psychic processes, sensa- 
tions) and material events (brain processes or the external stimuli 
which cause them). It is clear that Fechner was greatly stirred by his 
new insight, excited enough to spend the next decade of his life in 
careful experimentation, relating the intensities of sensations to the 
corresponding magnitudes of their stimuli. He came presently to be- 
lieve that, if the intensity of a sensation is to be increased by equal 
steps, the magnitude of its stimulus must always be increased by a 
constant ratio, i.e., sensation intensities of 4, 5, 6, 7, 8 might be 
aroused respectively by stimulus magnitudes of 5, 10, 20, 40, 80. 

In 1860 he published his great work, Elements of Psychophysics, 
showing how to measure sensations, and, in doing so, he believed that 
he had resolved the conflict between materialism and spiritualism. 
The world, however, thought otherwise. It noted instead that Fechner 
had actually succeeded in measuring mental phenomena and had 
thus opened the way to a quantitative science of the incorporeal 
events of consciousness. So often the contribution of a great man to 
the history of thought and discovery is something other than he had 
intended! 

We need not go into the history of these matters. Fechner was not 
alone in his novel researches nor was his thought entirely new. Away 
back in 1760 a Frenchman, Bouguer, had anticipated Weber's dis- 
covery. The great Helmholtz, physiologist and physicist, was busy 
measuring visual and auditory sensations while Fechner was at work, 
and a younger man, Wilhelm Wundt, was getting ready to "found" 
the new scientific psychology, that is to say, to give it a name ("phy- 
siological psychology/' later to be called "experimental psychology" ) , 
to write the first systematic handbook of the new science (in six huge 
editions from 1874 to 1911) and to create the first formal psycho- 
logical laboratory (in Leipzig in 1879). Suffice it to say that, when 
psychologists quote the timeworn sentence, "Psychology has a long 
past but a short history," they mean that, although psychology began 
with the Greek philosophers two thousand years ago and continued as 
mental philosophy alongside natural philosophy for a very long time, 



296 What Is Science? 

the new experimental psychology did not claim scientific status for 
itself until the middle of the nineteenth century. In those early days 
it was usually called "physiological psychology/' because it took over 
all the problems of sensation that the physiologists had been working 
on ever since they discovered that motor and sensory nerves are dif- 
ferent. So it comes about that our present interest lies almost wholly 
in the achievements of the last one hundred years. 

The present nature and range of experimental psychology is to a 
very considerable extent a consequence of psychology's history. The 
largest body of modern established fact lies in the field of sensation 
and perception, simply because that is the oldest interest, the topic 
in which research had already been started by the sense-physiologists 
before the new scientific psychology came into being in the 1860s. 
At first there were no satisfactory ways of measuring learning and 
memory, but Ebbinghaus, inspired by Fechner's success with sensa- 
tion, published the first measurements of learning in 1885. He found 
that you can measure learning by counting the repetitions necessary 
just barely to master a given material or skill, and that the memory 
for such learning can be measured by noting how many fewer rep- 
etitions are required to master the same material or skill again at a 
later date, when forgetting has weakened but not entirely destroyed 
the original learning. These early methods, crude as they were, showed 
that memory and learning can be studied experimentally and also 
revealed the general nature of the functions for learning and for- 
getting. Modern methods, using as subjects children and adults, rats 
and pigeons, are more complicated as well as more precise. Pigeons, 
for instance, can learn certain rules for obtaining food by pecking 
at a button. They peck away all night, rewarded systematically with 
food by a machine, with their peckings all recorded on a tape. Thus 
learning, in an age of electronic gadgets, has become the most active 
field in experimental psychology. 

The new psychology of observation and measurement had, by the 
end of the century, moved on from the investigation of the problems 
of sensation and perception to the study of learning; yet it remained 
insufficient for a complete description of man's thought and conduct. 
Men are activated by motives, by intentions, purposes and wishes, 
which are something more than learning and indeed affect learning 



Psychology 297 

as well as thinking and acting. It is not really possible to understand 
about human nature until one gets at the causes of its action. Psy- 
chologists did not know how to go ahead until they came upon the 
fact that psychology has to deal with unconsciousness as well as con- 
sciousness. Then they began to make a new kind of progress with 
what came to be called "dynamic psychology," the psychology of 
motivation, most of which works unconsciously. 

No one did so much to promote this new research as Sigmund 
Freud, whose psychology of wishing first came to attention about 
1900. Freud himself was not a conventional experimentalist. His lab- 
oratory was the consultation room, and also the bedchamber, where 
people had their dreams. A dream may be a partial revelation of what 
was previously a wholly repressed wish that was his great discovery 
at the turn of the century. So often man docs not know what he 
wants, especially when the unknown wish finds itself in conflict with 
some other socially approved wish. For instance, a man might hope, 
without consciously admitting it, that his father would die so that he 
could inherit his patrimony, and at the same time wish to have his 
father remain in good health because he is fond of him and admires 
him. Then the suppressed wish for his father's death might be half 
revealed in a dream and ultimately be brought completely to light 
by the laborious techniques of psychoanalysis. Even if the wish were 
not revealed at all, its existence could make the wisher feel guilty 
without his knowing why. For such reasons Freud developed the 
conception of the unconscious as the repository for repressed wishes. 

The experimental psychologists were not quick to accept Freud's 
brilliant contribution to psychology, but they soon discovered in- 
dependently that the key to creative thinking lies in the unconscious, 
in the predisposition with which the thought-problem is approached, 
a predisposition that is usually unconscious both before and during 
its operation. When later experimental psychology took up with the 
new concepts of a developing psychoanalysis, psychology had rounded 
itself out, at least so far as the mind and behavior of the individual 
were concerned. There was still waiting for advancement social psy- 
chology which deals with the interaction among people. 

The first generations of scientific psychology were therefore percep- 
tion-lcarning-motivation, and the range and stability of each of these 



298 What Is Science? 

important fields can be seen now to be roughly proportional to its 
age. Motivation, the youngest field of study, is the least secure. 

Now that we have briefed ourselves on experimental psychology's 
three most important topics, we finally get around to asking the basic 
question: "What is psychology about?" The answer to that question 
is different in 1950 from what it was in 1900. In the first half-century of 
scientific psychology's existence it was understood that consciousness 
was the object of study in psychology, consciousness and the manner 
of its dependence on the brain. Two hundred years earlier, in 1650, 
the philosopher-physiologist Descartes had made the distinction be- 
tween mind and matter clear, and everyone thereafter continued to 
accept his basic view. Mind, said Descartes, is unextended sub- 
stance; it lives in the body but takes up no space there; it may even 
be immortal and live on when the body dies. Matter, on the other 
hand, is extended substance; it occupies space; the body, the nerves 
and the brain are matter. Mind and brain interact. The nerves create 
sensation in the mind. The will directs muscular movement of the 
body. Fechner's psychophysics was actually a study of the relation- 
ship between consciousness and external stimulation, but he would 
have liked, had he known how, to study "inner psychophysics/' as he 
called the relation between consciousness and the brain. Altogether 
there was, up to 1900, no very serious doubt about what psychology 
was attempting. 

Then psychology discovered unconsciousness! It was a gradual proc- 
ess, this discovery, one of those developments which make you re- 
alize that the thinking of cultivated men and the progress of science 
are often determined by unrecognized forces at work in the culture 
at a particular time. The Zeitgeist, as it has been called, the atmos- 
phere of the times, plays its role in insight and discovery and often 
accounts for the simultaneous independent discoveries, familiar to 
every historian of science. 

So Freud in Vienna was elaborating his concept of the Uncon- 
scious, discovering that wishes and motives may determine the 
thought and action of a person without his knowing what his own 
motives are. At the same time Kiilpe, an able but less well-known 
psychologist in Wurzburg, was discovering that thinking itself, crea- 
tive problem-solving, is largely or even entirely unconscious! Men 



Psychology 299 

form correct inferences without being able to say afterward how they 
formed them. His evidence was so little anticipated that years passed 
before its significance was grasped and still more years before it was 
related to Freud's simultaneously developed conception. 

In America, meanwhile, John B. Watson was founding behavior- 
ism, a school which argued that behavior, not consciousness, is the 
subject matter of psychology, that consciousness, even though it may 
exist independently of behavior, may nevertheless be safely ignored 
and should be ignored since the method of introspection, which 
had been used to get descriptions of consciousness, had proved un- 
reliable. Actually Watson came to this conclusion because he had 
been pursuing psychological research on the sensory discrimination 
and the learning ability of rats, where behavior is what is directly 
observed and consciousness can only be inferred. Quite naturally he 
proposed that psychologists should extend to human subjects the 
methods that had proved successful with animals. So it was that 
these three synchronous trends Freud's, Kiilpe's and Watson's 
converged. Motive is usually unconscious, said Freud. Thought and 
creative insight, when brought under experimental control, turn out 
to solve their problems and reach their goals automatically, depend- 
ing on an unconscious predisposition which controls their course: this 
was Kiilpe's contribution. In both cases you know about thought 
only from the eventual behavior or conduct of a motivated thinker. 
Behavior is the chief datum. Still later Watson made the point that 
not only motivation, but also learning and discriminatory sensation, 
can be studied as behavior in animals without regard to conscious- 
ness. 

The victory of behavior over consciousness as the primary datum of 
psychology is perhaps not yet complete the world around, but there 
are two factors which have favored it in the past and are likely to 
promote it in the future. 

The first of these is to be found in the spirit of America. Experi- 
mental psychology began in Germany and for the first half-century 
Germany led, with America a close second. In no other nation was 
development so rapid as in these two. By 1920 America had gained 
the lead. The use of psychological tests in World War I accelerated 
the American development. Then Hitler crippled German science and 



300 What Is Science? 

after that the demands for psychology in World War II forced the 
science far ahead in the United States. In 1917 the American Psy- 
chological Association totaled 336 members. In 1955 it had about 
13,000, having increased steadily, like compound interest, at the rate 
of ten per cent per annum since its founding in 1892. But America 
is a practical country, a pioneer country in which settlers not so long 
ago wrested their living from stubborn nature. That is why America 
took so readily to a practical philosophy like pragmatism and at first 
put engineering ahead of science. So Americans were more concerned 
with what people do than with what goes on privately inside their 
heads. For that reason behaviorism found a ready acceptance in the 
New World, as it could not in a Germany accustomed since Kant to 
idealism; and, with America gone behavioristic, classical psychology 
could but surrender to majority rule. The small minority who clung 
to consciousness as the chief subject matter of psychology was for 
the most part sequestered in Europe, far away from this astonishing 
multiplication of psychologists in America. 

The other influence that favored the identification of behaviorism 
with psychology was more subtle and also more effective. Watson had 
said that, after all, introspection is behavior, a kind of verbal be- 
havior. Later P. W. Bridgman, the physicist, was to argue for opera- 
tional definitions of scientific concepts, for the notion that a scientific 
datum like distance or an atom is defined wholly by the operations 
that are used to identify or describe it in scientific observation. The 
Vienna School of logical positivism provided for this view a philo- 
sophically sophisticated background. Then, about 1930, the Ameri- 
can psychologists took up with it. Consciousness thus became that 
which is reported in introspection, and thus any language that an 
organism uses to describe its own characteristics. So a rat reports on 
its capacities by the errors it makes in learning a maze, and an ape 
by its insightful behavior in piling two boxes, one on top of the 
other, to enable it to reach the suspended banana. Similarly man 
reports on his sensory capacity by pressing a key when he sees a cer- 
tain color and not pressing it when the color is slightly different, and 
on his learning ability by making only so many errors when he tries 
to repeat a list of nonsense words after saying them over twenty times. 

The fundamental principle here is that science deals only with 



Psychology 301 

public information, and, whatever private consciousness may be like, 
it gets into science only by publication of some sort by the words 
or gestures or other behavior of the organism to whom the con- 
sciousness belongs. Even the unconscious is tapped by the psycho- 
analysts only through the use of words or other behavior. This bit 
of behavioristic logic put the American psychologists at case, allowing 
most of them to go all out for behaviorism. Introspection still exists 
in psychoanalysis, in social psychology, in the study of perception, in 
psychophysics, but nowadays we know that introspection is a kind 
of behavior; it is communication by physical signals which mean 
something crucial about the organism the organism that was con- 
scious in the 1850s but is only behaving in the 1950s. 

So now it is conventional to say that psychology studies behavior, 
even though, quite often and quite properly, it seems to be talking 
about conscious experience. 

With the general area of psychology thus mapped we can turn to 
some of the more important fields of psychological research, sampling 
each for the kinds of facts and laws which have emerged within it by 
the use of the experimental method: in other words a sampling in- 
ventory of the new experimental psychology that is now only a hun- 
dred years old. 

1. Psychophysics. Psychology's long attack on the problems of 
sensation is best illustrated by examples from psychophysics, the dis- 
cipline that Fcchncr founded in his unsuccessful attempt to spirit- 
ualize nineteenth-century materialism. Psychophysics includes the de- 
termination of thresholds both the absolute threshold, which is the 
least stimulus that can be perceived, and also the differential thresh- 
old which is the least perceptible difference between stimuli. A 
great mass of research on the absolute thresholds reveals the human 
being as an astonishingly sensitive indicator of small changes in the 
physical world. 

In vision the threshold for light is about 0.3 microwatts for a large 
stimulus a meter square in the center of the field of vision when the 
eye is most sensitive because it has been left in the dark for half an 
hour. That is the power that would raise a 3-gram weight one-hun- 
dredth of a millimeter in one second. Not very much power. Never- 
theless it is about a thousand times as great as the threshold out at 



302 What Is Science? 

the extreme edge of the visual field where the value is only about 
0.0003 microwatts. If the light is concentrated on a tiny area, as it is 
for the image of a star, the threshold is still lower, something like a 
hundred million-millionths of a watt. An erg is the energy required 
to raise one gram a thousandth of a centimeter, yet such a threshold 
star would have to shine on a human eye for forty years before it had 
delivered an erg of energy to it. Actually the human retina at its edge 
is thirty thousand times as sensitive as the most delicate radiometer 
which physicists use for detecting radiant energy. 

Is the ear less sensitive than the eye? No; if anything, it is just a bit 
better. If you compute the maximal sensitivity for each under the 
very best conditions, you discover that the power that will just affect 
the retina of the eye a star on a dark night seen out of the corner of 
the eye is about 0.000,000,010 microwatts, whereas the power that 
will just affect hearing at middle tonal pitch which is the most sen- 
sitive region is about 0.000,000,004 microwatts. Those figures may 
not, however, be exact. It is better to say that both eye and ear are 
amazingly sensitive when conditions are right. Then the eye can per- 
ceive a bare half-dozen quanta of light, a quantum being the smallest 
unit of light that a modern physicist can conceive of. If the threshold 
for the ear were reduced to one-quarter of the value indicated, it 
would be possible to hear the movements of the molecules of the 
air, to perceive a movement of the air less than the diameter of a 
molecule of hydrogen. 

All the evidence points to the fact that smell is as accurate and 
rich a sense as sight and hearing, that man may still have the olfactory 
capacity of some of his smell-minded mammalian ancestors. Catarrhal 
conditions may limit his sensitivity, and modern Western culture 
tends to turn attention away from smell. Nevertheless it is possible 
for a clear nose to smell one part in fifty thousand million of the 
putrid substance called mercaptan, to perceive as little as 0.000,000,- 
000,002 grams of this substance. 

The other senses, such as taste, pressure, cold and warmth, are not 
so keen as these three, but their thresholds are still surprisingly small. 
In general, the psychologists have discovered that man has a greater 
capacity for fine perception than he ordinarily uses. In World War II, 
when the senses had to be used to the limit in the competition for 



Psychology 303 

victory, some of the ways for obtaining maximal sensitivity were 
worked out in careful research. An airplane night flier, to take one 
example, needs to know just what conditions will make visual sen- 
sitivity greatest, and also the situations in which even the best vision 
can fail him, the situations in which he must rely on other informa- 
tion if he is to escape disaster. 

There is one exception to the above generalization: man employs 
visual space perception to the full limit of his capacity. The human 
eye can perceive as a black line a very dark distant wire against a very 
bright background when the width of the wire subtends at the eye 
only one second of arc. A second of arc represents on the retina about 
one-fifteenth of a thousandth of a millimeter and that is only about 
one-fortieth of the distance between the separate nerve endings. How 
is it possible to get such fine perception? On the retina the image of 
the wire is just a long straight blur, due to the optical imperfections 
of the eye and the random scattering of the tiny sense organs; but 
the brain translates such a long continuous blur back into a black 
line with edges sharp against its background. So the brain restores 
some of what the eye loses. 

Man uses the visual portions of his brain to their limit. In hearing, 
the two halves of the brain pretty nearly duplicate each other. One 
half either half is needed for hearing and the other is a spare. The 
loss of the auditory center on one side does not greatly impair hearing. 
In vision, on the contrary, both halves are needed. The visual center 
in the left half of the brain works for the left halves of both retinas, 
which do the seeing for the right half of the field of vision (since the 
eye is a camera which reverses the perceived field, right for left). Any 
injury to the visual area in either half of the brain necessarily results 
in a spot of blindness. 

You often hear it said that all science is empirical, that psychology 
and physics both go to the same experience for their primary data. 
That is true. The physicist Ernst Mach once wrote a book to show 
that both psychology and physics are different kinds of analysis of 
the same kind of sensations. But physics is wise. It is not interested in 
the sensations themselves but in what they indicate, and so it uses 
the most accurate kinds of sensations for its supply of information, 
that is to say, it uses visually perceived lines. That is why you hear it 



304 What Is Science? 

said: "Yes, physics is empirical; it is an empirical science of scale read- 
ings," for, whenever possible, physics reduces its scientific observa- 
tion to the visual perception of a scale. The ear may be able to 
perceive a little less energy than the eye under optimal conditions, 
but no perception in any of the human senses is so effective as the 
eye when it comes to perceiving spatial pattern and spatial difference. 

2. Perception. In recent years there has been interesting exper- 
imental work on what has come to be called object constancy. The 
human brain has built into it various properties which enable it to 
correct immediate sensory impressions in such a way that the man who 
owns the brain gets a truer perception of the outside world. Helm- 
holtz called these corrective mechanisms "unconscious inference/' be- 
cause the brain assembles a variety of data in order to build up the 
best and truest perception. 

A good example is 3-D perception in the modern stereoscopic 
movies which show depth. Here you have two pictures, one taken 
from the point of view of the right eye and the other from the point 
of view of the left eye. A tridimensional scene looks different when 
viewed from different angles, and it would be possible to measure 
the discrepancies in two such pictures so as to compute the depths 
in the third dimension trigonometrically. The brain, however, nor- 
mally makes that computation for the disparity of view between the 
two eyes instantaneously, so that we see the depths just as they are, 
or exaggerated if the two pictures are taken from points farther apart 
than the separation of the two eyes. You can take successive pictures 
of the ground from an airplane, view each picture stereoscopically 
with the proper eye, and see the perspective of the distant scene below 
that you would get if your eyes were a hundred yards apart and 
40,000 feet above the ground. The important point to note here is 
that the brain and the two eyes together get a truer perception than 
can either eye alone, for together they make up 3-D vision, whereas 
each retina alone has only 2-D vision. 

One of the most familiar and best understood cases of object 
constancy, where the brain corrects the eye in the interests of truth, 
is what is called size constancy. If you are looking at a man 20 feet 
away and he walks off to a distance of 40 feet, his image on your 
retinas shrinks to half its original height, but the perception of him 



Psychology 305 

does not shrink. He looks just as tall, and will continue to look just 
as tall if he walks away to 200 feet. Certainly a chap who is six feet 
tall when twenty feet away does not get to seem seven inches high 
(one-tenth as tall) when 200 feet away. The brain, however, needs 
information or it cannot perform this calculation; it needs to "know" 
the distance. If you deprive it of all its clues to distance, let it use only 
one eye, render invisible all perception of objects that would provide 
the clues of visual perspective, work with unfamiliar objects, like faint 
disks of light in complete darkness, then object constancy fails and a 
disk twice as far away does indeed match the size of a near disk of half 
the diameter. But give the brain its necessary data and it does its 
corrective job unconsciously and instantly. 

3. Reaction. Even though the psychologists of the late nineteenth 
century were primarily interested in consciousness, certain crucial 
facts of behavior did not escape them. Reaction time was one of 
these. Indeed, the pioneer work in this field was performed by the 
astronomers long before there was any scientific psychology as such. 

In 1796 the Astronomer Royal at the Greenwich Observatory dis- 
missed his assistant because the assistant could not make accurate ob- 
servations of the times of stellar transits, that is to say, he could not 
estimate accurately, while listening to the ticks of a seconds-clock, the 
fraction of a second at which a star, seen in the field of the telescope, 
crossed a given cross hair. Actually all the Astronomer Royal knew 
was that he and his assistant did not agree, and twenty-five years 
later a German astronomer named Bessel undertook to examine this 
situation further by comparing his own observations with those of 
another equally distinguished astronomer. The two men differed by 
almost a whole second, an astonishingly large amount. That led the 
astronomers to begin the study of individual differences between ob- 
servers "personal equations/' they called them in order that they 
might correct the observations of one man to agree with the observa- 
tions of another. 

Another twenty-five years went by and electric currents had be- 
come available for scientific use, and electromagnets, and electrically 
operated chronoscopes which would measure time-intervals to a thou- 
sandth of a second. Then it became possible to measure absolute reac- 
tion times, to see how long it took an observer to press a key after a 



306 What Is Science? 

signal had been given. The astronomers at first had been able only to 
compare one observer with another; now they and presently the psy- 
chologists could measure the actual time for a signal to be perceived 
and for a movement to be made in response to it. These reaction 
times, studied intensively in the psychological laboratories, turned out 
in the 1870s and 1880s to vary with the individual reactor, with the 
sense-department for which the signal is given, with the degree of 
complication in the stimulus or the reaction, and ultimately with the 
preparatory attitude of the reactor. 

The times of the simplest reactions were of the order of one or two 
tenths of a second, and it was found that there is a sensory type of 
reaction, when the reactor is prepared in advance to make sure of the 
nature of the stimulus before he reacts, and also a motor type of reac- 
tion when he is set to respond as quickly as possible without waiting 
for full cognition of the stimulus. The sensory type takes something 
like 0.2 seconds and the motor type nearly as little as 0.1 seconds. 
The quicker motor type is, however, less accurate. It may be touched 
off by the wrong stimulus or go off prematurely without any observa- 
ble stimulus. The false starts in the hundred-yard dash are of the 
motor type. 

Historically this discovery marks the beginning of the experimental 
psychology of motivation because it shows how an initial predisposi- 
tion to perceive the stimulus accurately or to go off just as quickly 
as possible can affect subsequent psychological events. Predisposi- 
tions are attitudes, are essentially wishes or needs or motives. They 
have their effects on almost every psychological event and, as we 
have noted, are more often unconscious than not. 

The modern uses of reaction times are many. If, in a test of mem- 
ory, an association comes more quickly by a few hundredths of a 
second, it is judged to be stronger. The association test for crime 
detection and for the recovery of repressed ideas makes use of the 
converse fact that it takes time to inhibit the strongest and most 
immediate response which, if given, would reveal the guilt or the 
repression. Reaction time is used to measure degree of attention: a 
distraction is really working if it slows down time of response. Air- 
plane pilots, chauffeurs and the operators of many kinds of machines 
are tested for reaction times. The best chauffeurs have intermediately 



Psychology 307 

long times; accidents increase when their times are too slow or too 
fast. 

4. Learning. As we have already seen, the experimental study of 
learning did not begin until Ebbinghaus' researches in 1885. The 
British philosophers had already established without experiments cer- 
tain laws of association, which were to all intents and purposes laws 
of learning. The chief of these was the law of frequency of contiguity, 
and Ebbinghaus based his work on this principle, that the more often 
two ideas are together in consciousness, the more often a new 
arousal of one will rearouse the other. To get fairly uniform material 
with which to work he invented nonsense syllables, three-letter items 
like BAP, WEG, FID, TOX, RUV, and had his subjects (himself 
for the most part) repeat series of these syllables until they just 
barely knew them. Actually he found that frequency of happening to- 
gether does not work in any simple manner. If you double the length 
of a series of syllables, you have to repeat it oftener to learn it, that is 
to say, you have to increase the frequency of the contiguity between 
each pair of successive syllables. The adding of extra syllables weakens 
the connection formed between the others. 

What holds for ideas may also hold for behavior, as Pavlov, the 
Russian physiologist, found out when he discovered the conditioned 
response at the beginning of the new, bchavioristic twentieth cen- 
tury. If you teach a dog to recognize the sight of food so that his 
mouth waters when he sees it, and if you then sound a tone regularly 
just before he sees the food, he will presently anticipate the food; 
that is to say, his saliva will flow when he hears the tone and before 
the food appears. The salivary response to the sight of food is said 
then to have been conditioned upon the sound of the tone, and the 
conditioning is, in part at least, a result of the frequency of con- 
tiguity between the hearing of the tone and the seeing of the food. 

In this manner you can investigate all the laws of learning and 
memory, as well as all the laws of sensation. You can find out by 
experiment how faint a tone can become and still remain a condi- 
tioning stimulus, and how well the dog can discriminate between one 
tone and another by salivating for the proper frequency and not 
salivating for a slightly different frequency. Pavlov called such a 
conditioned secretion of saliva "psychic juice," because most of the 



308 What Is Science? 

facts of learning and perception could be investigated in this manner. 
Later, when Watson founded behaviorism, he took over the facts 
and method of conditioning as a chief contribution to his new 
psychology that ignored consciousness. 

It is impossible to say whether psychology's swing away from the 
data of consciousness toward the data of behavior has been largely 
due to the suitability of animal subjects rats, pigeons, monkeys and 
apes for experimental work on learning and sensory discrimination, 
or whether causation has worked the opposite way. In either case 
learning has been the live fresh topic in experimental psychology 
since 1930 and most of the work has been done on animal subjects. 
One prominent investigator even dedicated his magnum opus to the 
white rat and he might have added, as so many authors say of their 
wives, "without whose help this volume could never have been writ- 
ten/' The rat learns the path to food through a maze, shows how he 
remembers what he has learned, demonstrates the aid or hindrance 
which knowledge of one maze is to learning another, or the effect 
of learning another on the memory of the first all of these situations 
being paradigms of what happens to learning and memory in college 
or in industry. The rat reports upon his sensory capacities by learn- 
ing or failing to learn to jump across a small abyss to a properly 
marked door. If he hits the correct door it opens and he is fed, but 
the wrong door is locked and makes him plunge uncomfortably down 
into a net. The pigeon learns to peck away at a button, often more 
than ten thousand times an hour, receiving food when he pecks in 
accordance with some prearranged schedule, for example, every forti- 
eth peck or every ten seconds. A pigeon can learn either of such sim- 
ple rules and adjust his pecking to them. Rat and pigeon they are 
perceiving, discriminating, learning, cognizing, remembering. 

One of the great advantages of using animals for subjects is that 
their brains can be operated upon, specific regions of the neural tissue 
removed or destroyed, and the effect upon learning or sensory dis- 
crimination noted. The two chief discoveries about the brain as the 
organ of what psychology studies consciousness or behavior have 
been these. (1) It is not safe to predict from lower animals to man. 
The lower forms need the cerebral cortex less than does man. For 
instance, removal of the visual brain areas in man renders him com- 



Psychology 309 

pletely blind, whereas their removal in the rat makes it unable to 
distinguish spatial patterns but permits it still to discriminate differ- 
ences in illumination. (2) Even in man not all the cerebral cortex 
is essential to learning and memory. A great deal of tissue can be 
destroyed, especially in the frontal regions, with little interference 
in the capacities of the person losing the tissue. Such losses make 
even less difference in lower animal forms. A dog with one cerebral 
hemisphere gone is astonishingly able, and even with both gone, al- 
though he lives a dull life without initiative, he gets along if he has a 
nurse to make sure that food gets into his mouth. On the other hand, 
a man with no cerebrum dies. As to where memories are kept or in 
what manner they are stored no one has an intelligent guess. The 
answer to this question has long been sought and still eludes the in- 
sight of even the most brilliant investigators. 

5. Emotion. There has been plenty of talk about emotion ever 
since William James in 1884 proposed the extreme hypothesis that 
we do not cry because we are sorry but are sorry because we cry. 
He was trying then to impress on his audience the fact that a 
thoroughgoing emotion always has in it a great many visceral changes, 
the perception of which constitutes an essential ingredient of every 
emotion. He was, of course, writing in the age when consciousness 
was psychology's main business. The important discovery about emo- 
tion came later in psychology's behavioral century. Studies of the 
emotions of dogs and cats resulted in what is called the emergency 
theory of emotion. A dog can be said to have an emotion in the 
presence of a cat, and conversely. A dog in a cat-perceiving state is 
found to have his sympathetic nervous system innervated. Such inner- 
vation has the effect of putting the organism the dog on a war 
footing, ready for violent action. It speeds up his heart, sends more 
blood to his voluntary muscles and less to his digestive organs, liber- 
ates sugar from his liver (the sugar that combats fatigue and increases 
strength), increases sweating (to keep the body cool under exertion), 
erects his hair (probably to make him look larger and more fierce), 
and stops all his digestive processes including the flow of saliva so 
that his mouth goes dry. (In India they judge a man guilty if his 
emotion makes his mouth so dry that he is unable to chew rice.) So 
to have an emotion is to be prepared for vigorous emergency action. 



310 What Is Science? 

Digestion can wait for more peaceful times. In this discovery we have 
the modern behavioral equivalent of James's organic stir-up in emo- 
tion, an inventory of the actual physiological changes themselves. 

6. Motivation. We have already noted that the third historical 
phase of experimental psychology is the period in which motivation 
became a problem for scientific attack. The pioneers were, as we 
have seen, Freud and Kiilpe, working independently on very differ- 
ent kinds of problems. Still earlier there had been the discovery that 
reaction time and type depend on the predisposing attitude of the 
subject before the reaction occurs. Freud worked out a psychology 
of unconscious wishes, the first thorough dynamic psychology. It was 
Kiilpe's student, Ach, who in 1905 discovered the determining tend- 
ency, as he called it. A determining tendency is a predisposition for 
association that is not dependent upon previous frequency of conti- 
guity. It acts, as it were, de novo. Ach found, for instance, that all his 
subjects, since they knew arithmetic, already had three common asso- 
ciations formed for the stimulus of an 8 over a 5. These associa- 
tions are the sum 13, the difference 3, and the product 40. The 
sum is the strongest association and the product the weakest. Never- 
theless Ach could, simply by asking his subjects to multiply, thus set- 
ting up in advance the proper determining predisposition, always get 
products as associations, never sums or differences, and that without 
any new practice in multiplying (without more frequency of con- 
tiguity). If you ask a man for opposites and give him the word 
black he will almost surely say white, but if you ask him for rhymes, 
then he will say tack or sack. Determining tendencies do not create 
new associations; they just make old weak ones, strong. If you ask 
for a rhyme for month you may get nothing; since very few have 
ever formed the association between month and (n + l)th, there 
may be nothing there to strengthen. 

Dynamic psychology does not talk much nowadays about deter- 
mining tendencies. It speaks principally of needs, drives and attitudes. 
The rat has a need for food, and food deprivation increases his hun- 
ger drive. There is really no such thing as unmotivated behavior, and 
hunger is the drive usually employed to produce action in animal ex- 
periments. Attitudes are prejudices, as the conservative attitude is 
different from the radical. One experiment has seemed to show that 



Psychology 31 1 

poor boys may actually see pieces of money as larger than do rich 
boys, a case of an economic attitude's affecting perception. Social 
psychology and the psychology of personality make broad use of the 
concepts of attitude and need. Quite early social psychology sought 
to list the primitive needs or instincts, but it is hard to distinguish 
between the primary inherited needs and the derived needs acquired 
through learning and the adaptation of the person to his cultural 
environment. 

In general, the primary needs are physiological, and they may also 
be vital in the sense that the organism dies if the needs are not sup- 
plied. Oxygen is a vital need of the organism, and so are water and 
food. A man can live for minutes without oxygen but not for hours, 
for days without water but not for weeks, and for weeks without 
food but not for months. Sleep is probably also a vital need, but 
mostly people do not die from sleeplessness; instead they go to 
sleep. Once an enthusiast, who thought sleep was a habit which he 
could break by practicing staying awake, actually did remain awake 
for more than nine days, but then he went to sleep. Sexual desire 
is a physiological need, activated by hormones in the blood, but it is 
not vital. Men do not die of sexual starvation. Activity is another 
physiological need which is not vital. It is these primary needs that 
drive the organism to action, and, when they are satisfied, the drive 
ceases until oxygen or water or food or sleep is needed again. 

Every theory of action holds that an organism in need is under ten- 
sion for satisfying the need. If an animal has in its repertoire of habits 
ways of satisfying a particular need, these habits are reinforced by the 
need and appropriate action ensues. On the other hand, if the ani- 
mal knows no solution under the circumstances in which it finds it- 
self, then it becomes restless and proceeds by trial and error until it 
hits upon a satisfaction. Satisfaction of a need, reaching a goal, al- 
ways terminates the drive for the moment. 

Most human needs are derived, built up within the social environ- 
ment in which a man lives. Different investigators whose tasks are to 
assess personalities develop different inventories of needs. One dis- 
tinguished group found it could get along with a list of thirty needs 
or attitudes the abasive, the achievant, the acquisitive, the affilia- 
tive, the aggressive, the ambitious, the autonomous attitude, and so 



312 What Is Science? 

on with twenty-three others. Other investigators have other lists. At 
times it seems as if need for aggression in the face of frustration 
were so universal as to be primary, but it is obviously not vital, nor 
physiologically based, nor is it inevitable since frustration can also be 
met with apathy. 

Needs are known to affect the form of perception, the nature of 
imagination, the degree of sensitivity and the persistence of activity. 
Every time we speak of wishful thinking or of a convenient memory 
we are expressing the belief that the existence of a need distorts the 
normal relation to reality of the person who has the need. Most of the 
disturbances of personality with which psychiatrists and psychoana- 
lysts deal, those that are classified as functional and not as organic, are 
disturbances of motivation of this sort. 

7. Ability. It is obvious that a man's personality is to a large ex- 
tent his motivational pattern, the inventory of his needs and attitudes. 
But his skills, abilities and aptitudes must also be added to make the 
whole psychological picture of the individual. An aptitude is a pre- 
disposition for acquiring a skill. Some people can learn languages 
more easily than can others; some have more aptitude for acquiring 
mechanical ability than have others. One kind of aptitude does not 
assure the existence of the other nor guarantee its absence. In gen- 
eral, however, abilities tend to be positively correlated. Some persons 
rate high in respect of many different abilities, and some low in re- 
spect of many. 

It used to be supposed that underlying all abilities there was a com- 
mon factor which was called general ability or intelligence. While it 
entered into different abilities in varying degrees, it was thought to 
have some part in practically all. That view is now becoming ob- 
solete, and, in a sense, the concept of intelligence might be said to 
be on the way out were it not so firmly rooted in school practices. It 
is indeed true that a large class of scholastic and academic skills, the 
bookish abilities of intellectual persons, show a high correlation with 
one another and with verbal abilities. The factor common to them 
is better called scholastic aptitude than intelligence, and it is cer- 
tainly a general factor among the abilities that are important in 
formal education. It was, of course, on school children and college 



Psychology 313 

students that the intelligence tests were originally tried out and 
calibrated. 

The modern tool for the analysis of abilities is factorial analysis. 
To use it you make up a battery of tests for whatever population you 
have in mind school children, soldiers, factory workers and you 
try to make the tests as different as possible but presumably covering 
all the activities important in your investigation. Then you administer 
them to as large a fair sample of the population as is practicable and 
treat the result by the new statistical procedures which select the 
factors common in determinable degrees to various tests, much in the 
way that physical forces are resolved into independent components 
by the use of the parallelogram of forces. So you come out with in- 
dependent factors a, b, c, d, . . . and statements of the degree to 
which each contributes to every test. Then you examine the nature 
of these contributions and give each factor the most plausible name 
you can think of. 

America's leading investigator in this field has worked out for 
eighth-graders and college students the following seven primary basic 
abilities in intellectual performance: (1) spatial visualization, (2) 
numerical quickness in arithmetical computation, (3) verbal compre- 
hension of ideas and meanings, (4) word fluency in speech, (5) 
memory facility for retention, (6) perceptual speed in observing de- 
tails, and (7) inductive ability to extract a rule common to a prob- 
lem. The U. S. Army in World War II constructed a General Classi- 
fication Test for its millions of soldiers. It avoided the word intelli- 
gence because that term seemed opprobrious in respect of those who 
scored low. This was a short test and it was based on the first three of 
the seven factors listed above. It worked well both for selecting the 
men of high general ability from those of low, and also for distin- 
guishing between verbal aptitude and mechanical aptitude, which is 
indicated by a high score for spatial visualization. 



Here we may stop, for we have had a look at at least one of the 
more important subjects of investigations in each of the seven most 
important topics of modern scientific psychology. The reader now 



314 What Is Science? 

knows what psychology is about, what psychologists think about and 
at what they work. 

Modern psychology is not, however, what Fechner was hoping to 
found on that October morning in 1850 when he had a vision of how 
to make the spiritual absorb the material in an age of materialism. 
His vision was sure enough to induce him to carry through an 
enormous amount of tough psychophysical experimentation during 
the next ten years of his life, but the world was not looking for a 
spiritualistic philosophy in 1850. Rather it was ready to snatch at a 
new science of psychology in the middle of a century which used to 
be called the scientific age. From Fechner's hands it took what he did 
not know he had, a new science of mind, for psychophysics must be a 
science if it measures, and it must be new if it manages to measure 
anything so incorporeal as sensation. Often in science the importance 
of research turns out to be something quite different from what its 
originator expected. In fact, the story of Fechner is the parable for 
the practice of basic research. If men are left free to pursue knowl- 
edge for its own sake, the new discoveries may be useful, yet often 
useful in wholly unanticipated ways. 

What would Fechner have thought if he had had a true view of 
whither his activities would lead by October 1950? In 1850 it would 
have seemed that psychology would remain the property of a rela- 
tively few scholars in the universities. In 1950 it had become the 
bread-winning profession of twenty thousand Americans and a few 
thousands elsewhere, with not more than a third of them in academic 
institutions. And as for materialism, the new science had gone al- 
most the whole way from what Fechner wanted, for not only had it 
forgotten about spiritual values, but it had also largely dispensed 
with consciousness, once its very reason for existence, and had be- 
come a physicalistic science of behavior. Perhaps it is well that no 
true vision of this future was vouchsafed Fechner. He might have 
been discouraged and never have given us psychophysics. But he 
would not have prevented psychology; that is sure. History, as Tol- 
stoy has made so clear, is the servant of no Great Man. Fechner was 
History's agent, not her master. Had he failed her, History would have 
found another man. 



ANTHROPOLOGY 



CLYDE KLUCKHOHN 



about 

Clyde Kluckhohn 



Clyde Kluckhohn was born in Le Mars, Iowa, in 1905. His early 
schooling included attendance at the Culver Military Academy 
and at Lawrenceville, after which he entered Princeton. Forced ta 
leave during his freshman year because of illness, he went to New 
Mexico to regain his health and spent a year, mainly on horseback, in 
the Indian country of the Southwest. "Fortune" he says, "landed 
me on the ranch of an educated and intelligent man who had a fairly 
good anthropological library and a lively intellectual interest in In- 
dians, I learned some Navaho and came to know more than casually 
Indians of a number of different tribes." These experiences are de- 
scribed in his first book To the Foot of the Rainbow, which appeared 
in 1927. He resumed his education at the University of Wisconsin 
where he graduated in 1928. "On leaving the university I was de- 
termined" he writes, "not to become a professor and thought of an 
eventual career in law, medicine or cattle ranching and politics" 
The award of a Rhodes scholarship enabled him to spend two years 
at an English university. While at Oxford he had "the wavering 
thought" of becoming a classical archaeologist and in 1930, on re- 
turning to the United States, "almost entered the Harvard Law 
School" But after another visit to the Southwest and flirting with 
the idea of becoming an Indian trader, he finally made up his mind 
to become an anthropologist. He attended lectures at the Sorbonne, 
wrote another book on the Southwest, studied anthropology at the 



about Clyde Kluckhohn 317 

University of Vienna and while there took the opportunity of 
being psychoanalyzed "inexpensively" and won a diploma in anthro- 
pology at Oxford. 

Kluckhohn began his teaching career at the University of New 
Mexico as assistant professor of anthropology from 1932 to 1934. In 
1935 he joined the Harvard faculty and the next year received his 
doctorate from the university. When he started teaching at Harvard 
there were two physical anthropologists on the faculty, the late 
Earnest Hooton and Carleton Coon; this fact led him to shift mainly 
to cultural anthropology. In 1946 he was made a full professor at 
Harvard. 

Kluckhohn s professional career has taken a broad and varied 
course. He has taught all branches of anthropology and has even held 
classes in anatomy; he has engaged in archaeological excavations in 
the Southwest, in England and Greece, and has published in this 
field, he has given courses in linguistics. 

Besides his academic activities Kluckhohn has since 1942 spent 
much time in government and administrative work. He has helped 
train military government officers, codirected an intelligence and 
psychological warfare group concerned with Japan, headed the Far 
East Policy Division of the Office of War Information, done odd jobs 
for the Office of Strategic Services, the Navy and other government 
departments, and for a period served on MacArthur's staff in Tokyo. 
In the fall of 1947 he organized the Russian Research Center at 
Harvard and he directed it until July 1954. The Center is the largest 
nongovernmental research institution dealing with the U.S.S.R. in 
the Western world; it studies all aspects of Soviet policy, with particu- 
lar emphasis on politics, psychology, economics and sociology. 

Among his writings are The Navaho (1947), Personality in Nature, 
Society and Culture, edited with Henry Alexander Murray (1948), 
and the prize-winning, Mirror for Man (1949), a popular study of 
what anthropology can do for world peace by promoting the under- 
standing of and respect for cultural differences. Dr. Kluckhohn is 
married his wife is a lecturer in sociology at Harvard and has a 
son who is a graduate student in anthropology at the University of 
Chicago. In his own opinion, his best work is a book on Navaho 
witchcraft and the concluding chapter in the volume The Excavation 



318 What 1$ Science? 

of B.C. 51. His academic distinctions include an honorary degree 
from the University of New Mexico, the Viking Fund medal for 
general anthropology and membership in the National Academy of 
Sciences. 



ANTHROPOLOGY 



CLYDE KLUCKHOHN 



Anthropology is the study of the similarities and differences, both 
biological and behavioral, among the peoples of the world from the 
dawn of human history to the present day. Anthropology excavates 
and analyzes the remains of past civilizations (archaeology); describes 
the evolution and present biological characteristics of our species 
(physical anthropology); traces the development and spread of cus- 
toms and technologies over the face of the earth, showing how these 
forms, arts, faiths and tools satisfy the psychological needs of indi- 
viduals and keep societies together (cultural anthropology); defines 
the varieties of human speech and the relationships among the 
tongues of men (linguistics). Its realm is thus immense; its ob- 
jective is to discover, by systematic and scientific means, the nature 
of this "human nature" about which we all talk so glibly. How has 
man come to be what he is? What is constant and what is variable 
in "human nature?" Can we explain the differences among human 
groups in terms of biology, of varying physical environments, of the 
accidents of history? More realistically, what approximate weight can 
be assigned to each of these factors both in general and under partic- 
ular circumstances? 

The following more specific questions will illustrate the range of 
anthropological enquiry: 

When and where were various plants and animals first domesti- 

319 



320 What Is Science? 

cated? By what routes and under what conditions did they spread to 
other peoples? 

Did the great pre-Columbian civilizations of Middle and South 
America learn how to work metals independently or did they get the 
idea or even the techniques from the Old World? 

Are all types of men, extinct and living, descended from the same 
ancestors or were there various separate lines of development? 

What are the present biological limitations and potentialities of 
the human species? 

How significant are the biological differences among existing hu- 
man populations? 

Is one type of physique more prone than another to specific kinds 
of organic or mental illness? 

Are the religions of peoples living in the tropics similar to one an- 
other and different from those of peoples living in the Arctic? 

Can styles in art or music be shown to depend upon economic or 
social organization? 

Are the child-training practices of a society reflected in typical 
adult personality? 

Is there any fixed rate at which languages ordinarily change? 

Is there a relationship between the nature of a language and the 
over-all way of life of a people? 

The diversity of these questions suggests something about the 
historical origin of anthropology which has been characterized as 
"the science of leftovers." The first anthropologists were specialists in 
geology, medicine, law and biology whose curiosity was intrigued by 
topics that were somehow left out of the then-existent sciences. An- 
thropologists today still refuse to be stopped by the artificial conven- 
tions that divide up academic subjects. They pay little attention to 
the line between "savage" and "civilized." There are only three 
things which unify anthropology: 

1. A focus on man in all his variation and similarity. 

2. A consistently comparative point of view. 

3. A stubborn conviction that history, physique, environmental 
situation, way of life, and language are all related in discoverable pab 
terns. 



Anthropology 321 



HUMAN EVOLUTION 1 

by S. L. WASHBURN 

Mammals have existed on earth for 60 million years and man's first 
mammalian ancestor was a four-footed beast about the size of a rat. In the 
millennia since then he has developed into the relatively giant biped of 
today. Paws changed to hands. The sense of smell was greatly weakened, 
while vision changed from a primitive condition in which each eye 
worked relatively separately and saw only black and white into the stere- 
oscopic color vision we think normal. The number of young was reduced 
from several to one at a birth, and the length of life was greatly in- 
creased. The method of locomotion changed at least twice and perhaps 
three times. 

The guiding factor in evolution is selection, and for most of human 
history man's fate was controlled in a way exactly comparable to that of 
other animals. But with the coming of the Ice Age some of the small- 
brained bipeds learned to use tools. Thereafter, adaptation, selection, 
migration, and the size of the group depended on the tool-making tradi- 
tions as well as on the biological endowment. In the latter phases of man's 
evolution it is impossible to study the physical changes without investi- 
gating the cultural changes with which they are inexorably linked. Espe- 
cially the great expansion of the brain, which we think of as uniquely 
human, seems to come after the upright posture and after the use of 
tools. 

Evolution reveals to us how our human nature, the basis for our way ol 
life, was built system by system over the millions of years of primate 
evolution. When our ancestors had evolved to the point where they could 
make tools, the process of change took on a new dimension and acceler- 
ated. If it were not for tools, mankind might be only a species of tropical 
bipeds, no more successful than the baboons. It is the importance of 

1 In view of my own lack of competence on this very specialized and tricky subject, 
I asked Professor Washburn, Chairman of the Department of Anthropology at 
the University of Chicago, to treat the topic. Very appropriately from the stand- 
point of this chapter, he stresses the origin of behavior rather than the details of 
the relationship between man and the various monkeys, apes, and other primates. 
C.K. 



322 What Is Science? 

culture in the late stages of human evolution which necessitates the close 
co-operation of the biologist and archaeologist. 

Although specialists agree on the main events of human evolution and 
their significance, they argue about the precise course of evolution. Has 
man been separated from the apes and monkeys for many millions of 
years, or is he a recent arrival, perhaps distinct from the apes for only 
a million years? Was man ever really an ape or is his origin so remote 
that his ancestors were more like monkeys? I believe that the close simi- 
larity in the arms of man and ape shows that our direct ancestors were 
arm-swinging apes, perhaps not very different from the living chimpanzee. 
However, this question cannot be finally decided until many more primate 
fossils are found, for the precise course of evolution can be revealed only 
by a moderately complete fossil record. In the meantime, the development 
of modern evolutionary theory and experimental methods helps to clarify 
the issues and to narrow the area still subject to disagreement. Further, 
the discovery of fossils depends less and less on chance and is becoming 
a planned search. As this process proceeds, the rate of discovery of fossils 
is accelerated. If the discoveries of the next ten years are as dramatic 
as those of the last, several of the most debatable issues may be settled. 

The History of Man 

The oldest-known tools have been found in deposits in South, East, 
and North Africa, in Europe, and in Asia. The earliest examples of 
toolmaking known occur in tropical Africa. They are primitive peb- 
ble tools made perhaps 600,000 to 700,000 years ago. Many authori- 
ties believe that their makers were the first true men whose skeletons 
have not yet been uncovered. However, the latest scientific review of 
the subject suggests that they may have been made by ape-men 
(Australopithecines) though perhaps of a different type from those 
whose physical remains have been discovered in considerable quan- 
tity in South Africa in recent years. The South African ape-men may 
have killed game with crude weapons such as sticks or bones. There 
is even some suggestion that they used fire, but this is still quite un- 
certain. The ape-men and the first true men may have had common 
direct ancestors, with the true men representing a more progressive 
line which evolved into larger-brained, toolmaking types. 



Anthropology 323 

Organisms and Stages Approximate Years Subdivision of 
of Cultural Development B.C. Geological Time 

Ape-men of South Africa 700,000-500,000 (?) Lower Pleistocene 

Earliest Pebble Tools of 700,000 Lower Pleistocene 

True Men 

Lower Paleolithic 700,000-70,000 Lower and Middle 

Pleistocene 

Peking Man 300,000 Mid-Pleistocene 

Neanderthal Man 150,000 and later Mid- and Upper 

(various varieties) Pleistocene 

Middle Paleolithic 70,000-35,000 Upper Pleistocene 

Modern Man 70,000 ( ? ) Upper Pleistocene (?) 

Upper Paleolithic 35,000-8000 Upper Paleolithic 

Mcsolithic 8000-4500* Early Post-Glacial 

Neolithic 4500-3000* Recent 

Bronze Age 3 500-1 500 * Recent 

Iron Age ISOOff.* Recent 

* For these dates the Middle East is taken as the point of departure. Figures for 
Europe and most other parts of the world would be later in some instances a 
good deal later. 

The earliest human skeletons (such as those of Peking Man and 
the Neanderthaloid races of Europe) reveal variable but uniformly 
brutish creatures. They may or may not be our ancestors. A few 
authorities still hold that modern man (who first appears, according 
to present evidence, about 70,000 years ago) evolved from these 
brutes. More students would hold that contemporary races carry at 
least some admixture with the earlier types. A third view is that the 
Neanderthal men of the Old Stone Age represent merely isolated 
survivors of a formerly widespread Neanderthaloid group, but that 
they were eventually exterminated by our own species whom we im- 
modestly call "wise men" (Homo sapiens). 

Man's brain began to outstrip the ape's brain only after his limbs 
and trunk had attained full human status. The critical primary 
adaptation that differentiated men as a distinct group was in the hip- 
bone. The size of the human brain increased as men adjusted to new 
ways of life. After the use of tools which presumably gave greater 



324 What Is Science? 

survival advantages to individuals who had large brains brain size 
doubled. The range in the cranial capacity of chimpanzees and goril- 
las is about 325 to 650 cubic centimeters, of the man-apes of South 
Africa 450 to 650, of Java Man 750 to 900, of Peking Man 900 to 
1200, of Neanderthal Man 1100 to 1550. The last range is about 
that of modern man. 2 Historic man has shown a more or less steady 
increase in average stature and a decrease in average head length. 

As human physique evolved, so did human culture: in technology, 
economy, art, religion and morals. For the more ancient periods we 
can only crudely sketch the evolution of tools and of ways of making 
a living. Archaeologists who specialize in the Old Stone Age distin- 
guish various types of assemblages of unpolished stone tools. Some 
of these archaeological "cultures" are found only in Europe, or 
Africa, or Asia; others are no respectors of continents. It is in the last 
phase of the Old Stone Age in Europe that we first learn some- 
thing, not only about tools, but also about religion, costume, and 
art. 

The lower Old Stone Age in Europe may have lasted 400,000 
years. The upper Paleolithic probably endured less than 30,000. Yet 
its advances in technology were far greater than were those of the 
longer period. Man employed a more economic but more sophisti- 
cated method of preparing flakes, 3 and fashioned a far greater number 
of specialized and standardized tools. He used bone, ivory, and antler 
extensively. He hunted with missile weapons and traps. Among his 
other inventions were the needle and thread, skin clothing, special 
fishing equipment, lamps of animal skulls or stone which he used in 
the dark caves where his paintings are now preserved. The earliest 
man-made dwellings are found in this era. The location of some 
settlements suggests a much more complex social life, including col- 
lective hunting. There is evidence for magic employed to increase 

'There is no conclusive evidence for Homo sapiens (modern man) before the 
third inter-glacial. 

*The earliest known tools were cutting instruments, made by breaking a roughly 
spherical pebble so as to get a sharp edge. Probably a little later are pear-shaped 
flint "hand-axes" about seven inches long and with detectable edges around their 
outlines. Contemporaneous though more frequently found in different regions 
were flakes of flint obtained principally by striking one rock with another so that 
good-sized chips "flaked" off. 



Anthropology 325 

the supply of food animals, for private property, and possibly social 
stratification. Art appears in various forms: finger-tracing, engraving, 
bas-relief, sculpture and painting. A wide range of red, yellow, 
brown and black shades are used. No true blues, greens, or whites 
have yet been observed. 

The European Mesolithic (Middle Stone Age) is an adaptation to 
a radically changed environment but does not differ too strikingly 
from the later Old Stone Age. Collecting of wild fruits, nuts, berries, 
and roots is more important in the economic life. Cemeteries show 
that fairly sizable communities of hunters and fishermen existed. 
There are indications of head-hunting, of cannibalism, and of some 
kind of chieftainship. The Mesolithic in northern Europe is as long a 
period as the whole of recorded human history (about 5000 years), 
but must be regarded as the final phase of an archaic way of life 
rather than as the direct harbinger of modern civilization. 

Our civilization derives directly from the New Stone Age (Neo- 
lithic) of western Asia and Egypt. Men changed from a wandering 
to a settled life. Formerly the Neolithic period was defined by the ap- 
pearance in the deposits of polished stone implements and contem- 
porary kinds of plants and animals. Today the significant criterion 
is taken to be the planned raising of food in contrast to the hunting 
and collecting of the earlier periods. In various parts of the Near 
East one finds rather suddenly at about the middle fifth millennium 
B.C. wheat, barley and sickle blades and the bones of cattle, pigs, 
sheep and goats. Other animals, among them the horse, appear to 
have been domesticated later and elsewhere. But present evidence 
suggests that the revolutionary inventions which made possible a new 
type of economy, town life, and vast changes in social organization 
and culture generally took place in the Near East during or prior to 
the fifth millennium B.C. Thus far only a few sites that may be 
transitional to the food-producing revolution have been excavated, 
and their dates are at present problematical. The earliest sites with 
good stratigraphy seem to be Jarmo in Kurdistan (Iraq), Tel Has- 
suna (northern Iraq), and possibly Jericho. It does seem clear that 
pottery, metals and writing are later than the domestication of plants 
and animals. 

A food-producing economy permitted a rapid increase in popula- 



326 What Is Science? 

tion. This in turn led to the spread of the Neolithic way of life. Colo- 
nies (perhaps of younger sons and daughters) had to be planted by 
land and sea. Within a few thousand years domesticated plants and 
animals, metallurgy, and town life had gone from the Near East 
along the shores of the Mediterranean as far as Spain and Italy and up 
the Danube into Central Europe. Eastward, Neolithic cultures spread 
to India, China, and elsewhere. Then follows the Bronze Age, which 
was succeeded by the Iron Age, and in the Mediterranean Basin we 
have arrived at the fairly familiar territory of classical civilization. 

The date of the first entry of man into the New World is still be- 
ing argued, though there is general agreement that the Eastern 
Hemisphere was the cradle of mankind. The conservative view is that 
human beings did not reach the Americas until after the final retreat 
of the Wisconsin glaciers (approximately 7000 B.C.). Most authori- 
ties, however, hold today that man arrived in the new world during 
one of the interglacial phases of the Wisconsin glaciation, or even 
earlier. Probably the first settlers in the Western Hemisphere slowly 
filtered down from the Arctic regions. Ancient sites in Alaska con- 
tain grooving tools and thin slivers chipped delicately from prepared 
flint cores that are very like artifacts characteristic of archaeological 
finds on the Asiatic-European side of the circumpolar region. Ten to 
fifteen thousand years ago the whole Arctic area seems to have been 
thinly populated by bands who had followed the animals clinging 
close to the retreating ice sheets. These bands gradually spread out in 
various directions wherever they found that meat was available. 

By 9000 B.C., according to this view, there were hunters in the 
North American high plains who made tools of distinctive type and 
rather similar to some of those found at Cape Denbigh, Alaska. By 
7000 B.C. human beings were living at almost the southern tip of 
South America. 

A generation ago almost all American scholars stoutly defended 
a kind of anthropological Monroe Doctrine. Man had reached this 
hemisphere from Asia via the Bering Strait region not much earlier 
than 2000-3000 B.C. All subsequent cultural evolution here had been 
entirely independent until after the arrival of Columbus with the 
possible exception of a not very influential earlier contact with Norse 



Anthropology 327 

voyagers. Attempts such as those of the British anatomist, Grafton 
Elliot-Smith, to show a connection between Maya architecture and 
sculpture and the artistic styles of Southeast Asia were howled down. 
Elliot-Smith wrote a witty defense, "Elephants and Ethnologists," 
in which he suggested that the Americanists simply refused to sec the 
obvious, but his and other arguments for transpacific connections 
were hardly taken seriously by American anthropology. There is 
little doubt that there was a factor of genuine bias here, for some 
relevant bits of evidence were conveniently ignored. For example, a 
last stronghold of the proponents of the anthropological Monroe 
Doctrine was the supposed fact that some of the distinctive features 
of the Old World Bronze and Iron Ages, such as the wheel, were 
completely unknown in the New World. Actually, wheeled toys 4 were 
discovered in a pre-Columbian horizon in Mexico as early as 1887 
and Middle American archaeologists have reluctantly come to the 
conclusion that some Maya pottery was wheel-made. 

Today professional opinion is less rigid. Development on these 
continents is held to be mainly indigenous, but the position of ex- 
treme isolationism has weakened. Aichaeologists recognize remarka- 
ble parallels between cultural elements in Peru and elsewhere in 
South America and some distinctive traits of cultures in Oceania and 
Southeast Asia. The archaeological remains indicate that, shortly after 
the time of Christ, certain Alaskan Eskimos obtained iron by trade 
from China and Korea. Their art also shows some striking resem- 
blances to ancient Chinese art. Some investigators grant the possibil- 
ity that Norse adventurers reached central North America two or 
three centuries before Columbus. Chinese junks may have been 
washed up on the shores of British Columbia or Washington. There 
seem to have been movements back and forth between this North- 
west coast and Siberia. Few today would maintain that the New 
World remained sealed off from the Old (except for successive mi- 
grations from Asia through the Bering Strait route) for fifteen thou- 

4 Little clay animals with semicircular protuberances instead of legs, each perforated 
to make a kind of bearing. The animals were accompanied by perforated clay disks. 
Linking the bearings and disks with a stick, the toys can be rolled back and forth 
on an even surface. A National Geographic Society expedition found (1940) in 
the state of Vera Cruz two more wheeled pottery toys which had axles running 
through clay cylinders on which the little pottery dogs (?) were standing. 



328 What Is Science? 

sand years or more. The disagreements now center upon how much 
contact there was and how much difference it made to cultural evolu- 
tion on this hemisphere. 

But these are speculations, and we may more profitably return to 
the facts. There were hunters on the high plains at least 10,000 years 
ago. Certain cave cultures of New Mexico and Arizona existed at 
approximately the same time. Some of the earlier simple hunting and 
gathering cultures changed very slowly, but maize was being raised 
in the Southwest by at least 1000 B.C. Pottery came nearly a thou- 
sand years later. At 1000 A.D. the classic civilization of the Pueblo 
Indians was full blown. To the far north the Old Bering Sea variant 
of Eskimo culture has dates as early as 300 B.C. The archaic horizon 
in Mesoamerica shows pottery, a calendrical system, writing, and well- 
developed religious cults during a period between roughly 1000 and 
200 B.C. The parallels of development between the Andean cultures 
and those of Mesoamerica are striking. The oustanding exceptions 
are the absence in South America of writing and of the conception 
of mathematical zero. The Incas did keep records and transmitted 
messages by knotted cords (quipus). By the time the Spaniards 
arrived the Inca and Aztec civilizations were both at a stage which 
has many analogies to Bronze Age society in Egypt and the Near 
East. 

Dating. Archaeologists employ perforce both relative and abso- 
lute datings. A human fossil or an artifact may be placed as earlier or 
later than others in the same undisturbed deposits. Or, its relative 
position may be given in terms of local or regional or inferred world 
sequences. A specimen may be given an absolute date either on the 
basis of its own properties or those of the deposit in which it was 
found or by geological or other correlation of the deposit with others 
whose absolute age has been established. 

Astronomy, geology, botany, chemistry, paleontology, geophysics 
and other natural sciences have all contributed ideas and techniques 
used by archaeologists to establish absolute or relative dates. The 
most exciting applications of recent years come from measuring the 
disintegration products of radioactive elements. The radioactive car- 



Anthropology 329 

bon (Carbon 14) method 5 is based upon the fact that organic mate- 
rials go through radioactive disintegration at known rates. It has been 
possible to date some hundreds of archaeological specimens ranging 
in age from a few hundred years to more than 20,000. The plus or 
minus error of these dates varies from 100 to 1200 years, but, for the 
older specimens at least, the method is far more accurate than the 
techniques hitherto available. However, the Carbon 14 method will 
not carry us back further than 30,000 years. For most of the 
Paleolithic we must still rely upon astronomical, geological, paleon- 
tological, and geophysical correlations. 

It is possible to mention only one other specific technique, that of 
dating by tree rings. 6 By comparing the rings in a given beam with a 
master chart one can discover the year in which this tree was cut. If 
the beam has not been re-used, one can thus determine the year in 
which a structure was built. Tree-ring dating is reasonably accurate, 
but a trustworthy master chart cannot be worked out in all climatic 
areas. 

Anthropological linguistics also helps greatly to unravel the rela- 
tionships of peoples and their movements in time. The newest 
method of linguistic dating was, curiously enough, suggested by the 
Carbon 14 technique and involves an application of the same theo- 
retic principle. The fundamental everyday vocabularies of languages 
change at a relatively constant rate. The percentage of such words 
retained in common by related languages gives a good estimate of 
the time elapsed since the linguistic community broke up into two 
or more segments. One takes several hundred basic words (numerals, 
father, mother, water, heart, day, night, long, short, and the like) 
and sees how many are phonetically alike in the two languages being 

"Carbon 14 (contained in charcoal, vegetable matter, bone and shell) disappears 
from dead tissue at a constant rate. In about 25,000 years most of it is gone. 
Therefore, if a fragment of organic matter is found to have about one-half the 
amount of carbon 14 found in living tissue, the fragment may be estimated to be 
roughly 12,500 years old. 

6 In a region where there are sharp variations in moisture from year to year, tree 
rings of varying widths and shapes occur. By examining enough specimens one can 
construct a patterned sequence over a series of years (from about 1 A.D. to the 
present in New Mexico-Arizona ) , The pattern of rings in any particular tree can 
then be matched against the total sequence to see exactly where it fits in. 



330 What Is Science? 

compared. Sixty-six per cent of the basic words ought to be recogniza- 
bly similar if the languages were a single language one thousand years 
ago. This technique (which goes by the formidable name of "glot- 
tochronology" or "lexico-statistic dating") has, for example, indicated 
that the Eskimo and Aleut were a single language about 2900 years 
jgo and that certain Indian tribes in the Southwest which we know 
historically as quite distinct constituted a common linguistic com- 
munity until around 1000 A.D. 

Archaeology obviously makes liberal use of natural science princi- 
ples and methods but it may nonetheless present itself to the reader 
more as "history" than as "science." "Science," he may say, deals 
with regularities and with process not with unique events. The an- 
swer is that, in anthropology, historical research is necessary to estab- 
lish the facts which can then be treated scientifically. For instance, 
the issue as to whether or not American Indian cultures developed 
independently of the major inventions and ideas of the Old World 
does not end as an academic squabble of antiquarians. It bears vitally 
upon important scientific generalizations as to the nature of man. 
Did the great ideas basic to civilization just "happen" only once? Or, 
is the nature of man as a biological organism such that, if he is 
turned loose in an isolated continent, roughly the same cultural steps 
will be taken in roughly the same order? We cannot yet answer this 
question definitively, but only more archaeological (i.e., "historical") 
work can solve this fundamental scientific question. 



Comparative Human Biology 

The human family has come a long way from the South African 
ape-men and from our heavy-browed forerunners of the Lower Paleo- 
lithic. However, except for a few apparently minor trends such as 
those toward the loss of "wisdom" teeth and perhaps the little toe, 
there is no evidence that evolution has appreciably altered human- 
kind for some thousands of years. The more recent changes have 
been due to various mixtures between diverse populations, to the 



Anthropology 331 

effects of movement into new environments, to improved nutrition 
and medical practices. 

The evolutionary process left certain scars upon the species. To the 
ancient adoption of upright posture 7 is traceable the frequency of 
various spinal and visceral ailments, for the accompanying mechani- 
cal adjustments have not been adequate. Difficulties in birth attend 
the fact that the heads of human infants have become larger, while 
the hipbones of women have grown shorter. Some students believe 
that man is no longer the unspecialized animal that had advan- 
tages in the evolutionary struggle 8 but is now overspecialized with 
respect to head, brain, and locomotion. 

Human beings appear to be very variable creatures. They are found 
in numerous colors and shades with a considerable range of hair form, 
nose shape, and the like. Height and general physique varies widely 
both between groups and among individuals within the same group. 
However, the comparative biologist is not as much impressed by 
human variation as is the laymen preoccupied with his own species. 
For an animal who wanders over the whole earth, adapting to almost 
every existing environment and mating with whomever opportunity 
affords and fancy dictates, the variabilities are comparatively super- 
ficial. In certain features, the gibbons from a single valley in Siam 
vary as much as all the races of man together. All human populations 
can and do interbreed with one another and produce fertile off- 
spring. An adopted infant, whatever the "race" of his biological par- 
ents, will acquire the language of his foster parents and can learn 
to ride a canoe, paddle a kayak or pilot a jet plane. 

But the fact that the similarities in human biology are vastly more 
massive than the differences docs not mean that the superficial but 
visible variations have not been socially important. On the whole, 
human groups have been distrustful or contemptuous of those who 

T Presumably because this was the most convenient form of locomotion for our 
large arm-swinging ancestors. 

8 Animals that are too highly adapted to a particular environment can hardly sur- 
vive when that environment (or other situations faced) changes too radically 
compare the enormous reptiles like the dinosaurs, who were suited only to the 
vast swamps of millions of years ago and who died out when the earth turned into 
deserts. 



332 What Is Science? 

looked, dressed, or behaved differently from themselves. And smug 
nineteenth-century thought in Western Europe seized upon the 
magic idea of evolution to justify an ordering of both way of life and 
"race" in a graduated sequence from "savage" to "civilized." 

There are recognizable physical types of humanity which to some 
extent correspond to the populations found in distinct areas and, to a 
much lesser extent, to linguistic and cultural groups. But: 

a) These types intergrade. That is, there are individuals who could 
equally well be classified as "Nordic," on the one hand, or as 
"Mediterranean" or "Alpine" on the other. 

b) They are based upon a limited number of features which have 
not been shown to be significant as far as the chief cultural 
capacities and limitations of the groups are concerned. Creative 
originality, ethical or humane standards of behavior, and the 
ability to absorb or communicate abstract knowledge are within 
the potentialities of all the living races of men. 

c) Classifications which are based upon different combinations of 
the small number of features ordinarily utilized do not alto- 
gether coincide. 

d) These types are not equivalent to the "breeds" of domestic ani- 
mals, because men for thousands of years have wandered and 
freely interbred. As a result, the members of practically any 
human group can be subdivided on the basis of appearance into 
more than one physical type. In any case outward appearance 
in the human animal is not a guarantee of hereditary sameness 
to the extent that it is in animal breeds. 

e) The popular (and the older scientific) classifications are based 
primarily upon such features as head form, stature, skin color. 
Unfortunately, in most of these cases the heredity mechanisms 
are complex and mendelian formulas have not been worked out. 
Hence the distributions of these characteristics in different 
populations are not amenable to quantitative genetic analysis. 

The familiar human "races" must be regarded as common-sense 
"types," based upon often misleading similarities in outward ap- 
pearance. They cannot be considered as scientific categories. 
This is not to say that all human populations are biologically the 



Anthropology 333 

same in all significant respects. There appear to be few all-or-none 
differences, but in the limited area (mainly the blood groups) where 
we have adequate information it is clear that there are some striking 
variations. For example, the Basques show a frequency of one blood- 
group gene which is twice as high as in any other known population 
and more than twenty-five times as high as in certain groups. African 
Negroes exhibit a tremendously high incidence of certain serological 
genes. There is a genetically determined condition of the blood cells 
known as "sickling" which is widespread among African Negroes 
and appears to be exclusively confined to Negroes and those who 
have some Negroid admixture. The genes responsible for thalassemia, 
hemoglobin c, and for the Henshaw antigen apparently have sharp 
geographical restrictions. Such genes are not known to be "linked" 
to other genes influencing temperament, mental ability, and the like. 
Nevertheless it is a reasonable assumption that such hereditary factors 
also will eventually be shown to have other than a random distribu- 
tion among populations. By the same token, it is most unlikely that 
any single group will be revealed to have a monopoly on "favorable" 
inheritance. 

In terms of mendelian genetics, "races" can be defined as popula- 
tions which differ markedly in their gene frequencies. Using ten or 
more genes, for which the frequencies and the hereditary mechanisms 
are known, the student of blood groups, W. C. Boyd, has tenta- 
tively postulated as major human races: Early European, European, 
African, Asiatic, American Indian, Australian and perhaps Indian 
(Hindu). This list does not differ too much from earlier classifica- 
tions based upon measurements and external features, but has the 
advantage of resting not upon sometimes illusory appearance but 
upon characters known to be inherited in specific ways. 

Physical anthropology in general is proceeding rapidly from meas- 
urement and description to the analysis of process and even to ex- 
periment. The physical differences that to some extent differentiate 
the various groups are brought about by a combination of processes. 
The only source of new hereditary traits is mutation the result of 
chemical changes in genes or structural rearrangements of the chromo- 
somes. But whether or not new inheritable characteristics become 
widespread in a population and spread to other populations depends 



334 What Is Science? 

upon a variety of factors, of which selection is the most important. 
Does a new gene give the individual who carries it an advantage in 
the struggle for survival? Does it increase his fertility directly? Does it 
give him a physical feature which is favored by the cultural norms of 
the group so that he can obtain mates more easily and thus be likely 
to produce more children? Selection (natural, social, and sexual) is 
the most significant process in the differentiation of populations. 
The following, however, are also of some importance: 

1) "race" mixture due to migrations or other events leading to 
interbreeding and hence to the alteration of the gene frequen- 
cies in a group; 

2) "genetic drift" 9 which, particularly in small and isolated 
breeding populations, may bring about either the complete 
extinction of certain genes in that group or the fixation of 
other genes at 100 per cent. 

Environmental influences vary in the degree to which they favor 
the survival of individuals possessing certain genes or combinations 
of genes. Human culture modifies the operation of natural selection 
as it works among other animals. Modern science and technology 
protects those who might not survive if the brute force of nature 
were alone operative. Even at the primitive level, culture powerfully 
influences the processes of selection, race mixture, and genetic drift. 
In some tribes twins are killed at birth, and the old and incapacitated 
are also done away with. Priests or "medicine men" arc required to 
practice continence over such long periods that they do not produce 
as many children as other males. In one clan in Madagascar all un- 
usually light-skinned children are killed, while in another clan of this 
same tribe the unusually dark-skinned are exterminated. Such cultu- 
ral practices as premarital promiscuity or frequent extremely hot 
baths may affect fertility. Some peoples are very intolerant of "race 
mixture"; others accept it readily. Genetic drift takes a sharper form 
if marriage within a small tribal group or band is rigidly insisted 
upon or if one must marry one's own cousin. 

Contemporary research emphasizes broad relationships rather than 
* The mathematics are too involved to explain here. 



Anthropology 335 

descriptive treatment of separate units of the body a legacy from the 
dissection of corpses. The following topics are representative: 

specializations of body mass, nose form 10 , fat and beard as responses 
to extreme cold; 

climatic selection of individuals of specific physical type; 
growth-control mechanisms; 

the fertility and life span of lanky and massive individuals; 
effects of soil minerals, protein-poor diet, early menopause. 

Constitutional anthropology is a subbranch of physical anthro- 
pology which concentrates on the individual. It is concerned with the 
relation between physique and behavior, including susceptibility to 
various kinds of diseases. Do the differences in size and shape that 
exist among individuals indicate any temperamental correlates and 
predispositions toward certain kinds of activity? The best-known ap- 
proach to these problems is W. H. Sheldon's "somatotypes," which 
classifies physiques on a three-dimensional scale. The study of consti- 
tution is the newest field in biological anthropology and, as usually 
happens with pioneer work at the frontiers of a science, one of the 
liveliest. Some students accept Sheldon's descriptive scheme but are 
most dissatisfied with the interpretations of the psychological and 
behavioral aspects. Others reject even the classification on the ground 
that the genetic mechanisms are unknown and that recent work in- 
dicates that (a) somatotypes change with age and diet, and (b) that 
the diagnoses (based on nude photographs) of the relative amounts 
of bone and muscle are not confirmed by radiological examination 
of the same individuals. 

Almost the only thing that students of constitutional anthropology 
agree upon today is that "there is something to it." Clinical experi- 
ence in medicine and anthropological researches using different 

10 Is, for example, a high, narrow nose, lined with thin mucous membrane charged 
with blood, an adaptation which prevents the excessive lowering of body tempera- 
ture of those breathing the very cold air of far northern lands? Certainly a nar- 
rower aperture reduces the volume of cold air admitted to the lungs. 



336 What Is Science? 

techniques and theories of explanation all converge upon the con- 
clusion that individuals of one type of body build are more prone 
than those of other types to engage in certain activities and to fall 
victim to certain illnesses. The most conservative position would be 
that this is true only for the more extreme forms of each physique 
type. At this level, there is now fairly satisfactory evidence for a defin- 
able relationship between body build and a few physiological and be- 
havioral variables. There are intriguing but as yet inconclusive studies 
of correlations between body build and mental disorder, ulcers, vari- 
ous kinds of arthritis, acute rheumatic fever, coronary diseases, dia- 
betes, and pernicious anemia. 

Human biology sets certain limits for human cultures. The more 
obvious of these are well known and have often been commented 
upon. Others remain to be explored. It is suggestive, for example, that 
the range for the number of kinship terms used in human societies is 
about the same as the range of the number of sound-classes (roughly 
but only very roughly represented by letters in alphabets) found in 
human languages. Every culture differentiates and names certain 
categories of relatives. In English we call both our mother's and our 
father's sisters "aunt/' In Navaho there are two distinct terms for 
these relatives. On the other hand, we used to have a kinship term 
in English "cousin german" (double cousin) for which there is no 
equivalent in the Navaho system. The point is that each culture uses 
somewhat different criteria in naming classes of relatives, but all cul- 
tures differentiate among roughly twenty and fifty such categories, 
with about twenty-five as the average number. Approximately the 
same thing holds for the sound types to which the speakers of each 
language react as "different." Some Polynesian languages have as 
few as a dozen distinctive sound classes ("phonemes"); no known 
language has more than seventy. Does this mean that the average 
human brain operates effectively only within this range of classific- 
atory units? 

Biology supplies the clues for many other aspects of culture. Popu- 
lar notions of space arise directly from the nature of the human 
frame (above, below, in front, behind, to this side, to that side i.e., 



Anthropology 337 

the six directions found in many cultures). Various dual divisions are 
based upon the existence of the two sexes; rites of passage, such as 
those of puberty, crystallize around biological events. Finally, it is 
plausible, though at present unproven, that the variations in the 
hereditary make-up of different populations lead to different selec- 
tions from the objectively open ways of developing and elaborating 
their cultures. For example, if there is an hereditary predisposition 
to a high activity level, presumably there will be vigorous attention 
to achievement, to "doing" as opposed to "being" and "becoming." 

But the process goes both ways. Warfare, as culturally defined, 
plays a part in both selection and fertility. Mutilations and regula- 
tions prohibiting or encouraging premarital heterosexual activity do 
likewise. Biological processes such as vomiting, sneezing, and fainting 
are produced by somewhat different stimuli in different cultures. 
Many Americans will vomit if they discover that they have, unknow- 
ingly, eaten rattlesnake meat, even though this is from a strictly 
biological point of view nutritious and easily digestible. In other 
cultures retching will follow upon failure to observe a ceremonial 
taboo. Cultural beliefs and values play a part in bringing about 
migrations, relative rates of inbreeding and outbreeding, nutrition 
level, infant care, preferences for the physical appearance of mates, 
and other practices that shape, directly or indirectly, the genetic 
process. 

Biological and cultural anthropology are both needed to under- 
stand the rise and fall of civilizations. }. L. Angel u in his studies of 
Greece through the centuries shows how the physical environment, 
biological factors such as hereditary elements and size of popula- 
tion, and cultural practices constitute a complex manifold. Culture 
growth and human change follow repetitive patterns: heterogeneity 
and invasion, fusion, and achievement. One of Angel's points de- 
serves special stress because it is a generalization supported by evi- 
dence from many parts of the world. Great civilizations appear to 
arise most often in areas where there is a great deal of both biologi- 
cal and cultural mixture. High cultures seem usually to be "mongrel." 

u A physical anthropologist who teaches human anatomy at Jefferson Medical Col- 
lege in Philadelphia. 



338 What Is Science? 

The Ways of Men 

Cultural studies investigate repetitive patterns of behavior which are 
characteristic of groups. Each culture consists of a linked series of 
man-made patterns and constitutes a selective way of thinking, feel- 
ing and reacting. A man, except at the level of reflexive behavior or 
under conditions of extreme biological stress, does not respond like 
a machine. He responds to the stimulus situation only as interpreted 
and defined in terms of conventions he has learned as a member of 
one social group or another. An Englishman and a Navaho Indian 
both notice a tree struck by lightning. The Englishman, at most, 
says to himself "Better stay away from trees during thunderstorms 
in this country." The Navaho begins to plan a ceremonial designed 
to protect himself against the dangerous experience of beholding a 
lightning-struck tree. The "objective" stimulus is the same; the reac- 
tions are quite different. 

"Culture/* a technical term, must not be confused with the more 
limited concept of ordinary language and of history and literature. 
To the anthropologist, a cooking pot or a deep freeze is just as much 
a cultural product as a sonnet or a great picture. The description of 
a culture may be compared to a map. A map is not a bit of land but 
rather an abstract representation of a particular area. If a map is 
accurate and one can read it, one can find one's way around. 

Cultural anthropology comprises many topics, among them primi- 
tive law, primitive economics, folklore, material culture, comparative 
music and the plastic and graphic arts. We cannot possibly treat all 
these interesting and important subjects; we can glance at only a few 
of the high points on culture change, social organization, religion, 
culture and personality, cultural relativity. 

The major cultural innovations (e.g., writing, metallurgy, and such 
mathematical ideas as zero and the calculus) appear to have occurred 
independently in only one or a very few cultures in the whole 
history of man. The spread of such discoveries then takes place 
through migrations, conquest, trade, and the activity of religious 
missionaries or through the diffusion of ideas by the printed word 



Anthropology 339 

or otherwise without direct personal contact. Detailed studies of the 
spread of the alphabet, tobacco use, cultivation of various kinds of 
food and similar cultural inventions have produced some general 
principles. New ideas and techniques do not fan out uniformly in 
all directions and at about the same rate from their center of 
origin. Rather, diffusion may be compared to a forest fire: things go 
where the wind blows and where impermeable barriers do not exist. 
Sometimes the high wind of fashion will lift sparks far over interven- 
ing areas. Sometimes the sparks smolder for a long time before they 
burst into flame. People have to be "ready" for new things. In 
general, gadgets spread more rapidly than do religious or political 
ideas. In many cultures women are more conservative than men. 
There is some evidence that individuals who are most disgruntled or 
maladjusted in their own societies will accept soonest new religious, 
political or social beliefs. 

Nevertheless, culture growth and change is by no means haphaz- 
ard. Even the fashions in women's clothes have been shown to be 
due not solely to the whims of the female and the machinations 
of Paris designers. In broad sweep the cycles are lawfully patterned 
in mathematically describable ways. 12 A. L. Kroeber 13 has also con- 
vincingly demonstrated that great artists and writers appear in civiliza- 
tions in "temporary bursts" and that the same sort of bursts in 
growth tend to characterize nationalistic development as expressed 
in successful political organization and expansion. Such periods en- 
dure for fifty years or for a thousand, though the shorter ones may be 
regarded as localized "pulses" in larger growths. 

Human beings need sometimes to be reminded how much they 

M The basic dimensions of the clothes of Western women alternate between max- 
ima and minima which average fifty years. In addition to these long trends there 
are also fairly regular short-term oscillations and well-defined periods of high or 
low variability of style. For details see "Three Centuries of Women's Dress Fash- 
ions" in A. L. Kroeber, The Nature of Culture, University of Chicago Press, 1952. 
"Alfred Louis Kroeber was for many years professor of anthropology and director 
of the Museum of Anthropology at the University of California in Berkeley. After 
he became emeritus there, he taught at Harvard and Columbia. He continues to 
be active in research and writing. He made a field trip as recently as 1952. He has 
contributed to all branches of anthropology and is generally regarded as the lead- 
ing anthropologist in the world today. 



340 What Is Science? 

owe to other human beings of far-off times and places. I am writing 
(Near Eastern invention) on paper (Chinese invention) in an al- 
phabet which began in the Mt. Sinai peninsula about 1200 B.C. We 
wear close-fitting garments which developed in cold climates rather 
than the loose, flowing robes of the tropics. We eat American Indian 
corn or Italian vermicelli (which really derives from China via Marco 
Polo) and drink South American cocoa. The interdependence of 
humanity is nowhere more dramatically illustrated than by a close 
study of cultural process. 

It is in the field of social organization that present cultural an- 
thropology (other than linguistics) is most exact. Some anthropolo- 
gists map with great precision what goes on in a small group. The 
observer presses a particular key on a machine whenever a particular 
person starts to talk. A chart is built up to show which person in a 
group talks the most, which talks the least, who most often initiates 
or dominates a conversation, who tends to respond passively. The re- 
sults often give a picture that is more objective and illuminating than 
could be obtained by asking the individuals about their relations to 
one another or from a description of the roles to which they are 
formally assigned in an organization (such as president and vice- 
president or lieutenant colonel and captain). These methods and 
other anthropological techniques are being applied with some success 
in the study of personnel problems and productivity in business and 
industry. Anthropologists who go into a factory or a department 
store try to observe what goes on among the employees with the 
same detachment that they bring to a primitive tribe. Ignoring any 
prior opinion they may have as to what motivates workers, they 
build up from the observation of behavior the regularities that are 
actually operative. G. P. Murdock 14 , among others, has taken a more 
academic approach to the anthropological study of social organiza- 
tion. From the evidence of changes in social structure, the "social 
laws of sexual choice," and the adhesions of certain features of so- 
cial life to one another, he has proved that: 

u Professor of anthropology at Yale. One of Murdock's greatest achievements was 
organizing and directing for many years the Human Relations Area Files. This 
undertaking, now a co-operative task of fifteen universities, has provided a cross- 
index by topics of the data now available on some hundreds of peoples scattered 
over the world. 



Anthropology 341 

. . . the elements of social organization, in their permutations and 
combinations, conform to natural laws of their own scarcely less 
striking than those which characterize the permutations and com- 
binations of atoms in chemistry or of genes in biology. 

The principal contribution of anthropology to the study of religion 
has been to show that religion is not normally something apart but 
rather flows into all areas of life and helps to maintain the adjust- 
ment of individuals and the solidarity and survival of societies. Some- 
one has said, "Human beings build their cultures, nervously loqua- 
cious, on the edge of an abyss." Religious life not only affords socially 
approved opportunities for personal expression and prestige but also 
gives a sense of security in a world which, seen in naturalistic terms, 
appears to be full of the unpredictable, the capricious, the acciden- 
tally tragic. In the face of chance and the unexpected, of wants, 
death, and destruction, all humans have a fundamental sense of un- 
easiness. By ritualizing their words and habits, they assure themselves 
that "reality" too is consistent. They mask the vast role of "luck" in 
human life by telling each other that such and such a thing happens 
because of something a supernatural being did or said long ago. In a 
world full of hazards, myths and rituals affirm that there is rhyme and 
reason after all. They give the future the appearance of safety by 
symbolizing the unbroken continuity of present and past. 

In both secular and sacred spheres, myths serve as statements of 
the right way to behave and the reasons therefor. For primitive 
people they constitute a literature which serves ends from intellectual 
and moral edification to simple entertainment. Both myths and rit- 
uals act as brakes upon the speed of cultural change. They stabilize 
and sanctify interpersonal relations. Even the "evil" side of religion, 
such as belief in witchcraft, has its functional significance. Nothing is 
more intolerable to human beings than to be persistently disturbed 
without being able to say why in terms that their fellows will under- 
stand or without being able to phrase the matter in such a way that 
some relief or control is considered possible. Witchcraft belief allows 
one to talk about his anxiety in terms that are acceptable and which 
imply the possibility of doing something about it. Witchcraft also 
channels aggression; in many societies it is a substitute for "race prej- 



342 What Is Science? 

udice" or similar scapegoating. Some cultural systems are more effi- 
cient than others in directing aggression into oblique or socially 
nondisruptive paths. But among many people witchcraft is the princi- 
pal answer to the problem that every society faces: how to satisfy hate 
and still keep the group solid. 

Anthropologists in the field of culture and personality attempt to 
answer questions of this type: 

Does a people's way of bringing up its children make a particular 
type of personality unusually common in that society? 

How much of any individual's personality is fixed by his biological 
constitution and how much depends upon his culture and his own 
experience in that way of life? 

Is there a connection between the mental illnesses characteristic 
of a given group and the social norms that this group enforces with 
special severity? 

In brief: What makes an Englishman an Englishman? an Ameri- 
can an American? a Russian a Russian? 

This field has suffered in the last decade or two from being so 
fashionable. Many publications have been hasty, overly schematic, 
and indeed naive. History and biology have been neglected to vary- 
ing degrees by many authors. In some cases there has been a ludicrous 
overemphasis upon a few aspects (or even a single aspect) of the 
child-training system. Too little notice has been taken of the effects of 
the isolation of particular children, or groups of children, from cer- 
tain segments of the cultures. In short, this anthropological specialty 
can be viewed as a promising infant, but a spoiled or overindulged 
one. 

Nevertheless, there are a few findings that can today be regarded 
as established. The first is the regrettably vague one that culture and 
personality are indeed interdependent. The second is that the influ- 
ence of a culture may persist long after the more obvious and exter- 
nally observable aspects of that culture have disappeared. Some Chip- 
pewa Indians dress and talk and make their living very much as do 
the white Americans with whom they go to school and work. Yet 
close study of their performance on psychological tests shows that 
their way of thinking and reacting is still much influenced by the 
aboriginal culture. There are also some negative conclusions. Much 



Anthropology 343 

can be explained only historically and in terms of situation. One can- 
not infer directly from a description of cultural patterns for child 
training to their consequences in personality formation. Parental at- 
titudes are often more important than methods, though the attitudes 
are, in part, also cultural products. A few quantitative studies on 
specialized topics, such as Whiting and Child's Child Training and 
Personality 15 , have been completed recently. In general, however, we 
know little more than we did a generation ago about how culture 
is "built into" a personality and whether some features of a culture 
are more crucial than others in forming distinctive personality types. 
Cultural relativity is one of the most influential concepts of modern 
anthropology. In a vulgarized form it has been taken to mean that 
behavior which is customary among any people is therefore justified. 
On this basis, we should have to accept slavery or Nazism as morally 
acceptable. What anthropologists have wished to point out in this 
area of their work is the broad spectrum of variability in human 
values and the necessity for considering all values and items of be- 
havior in their own context. However, it is true that for at least a 
generation anthropologists concentrated more upon cultural differ- 
ences than upon the equally factual similarities. It is also clear that 
insufficient consideration has been given to values as such and to 
systems of values. If the essence of culture is the selection of certain 
paths of life from among two or more that are objectively possible, 
the essence of this selectivity resides in the value system. Man is not 
only the tool-using animal; he is also the valuing animal, constantly 
making judgments of "better" and "worse" and behaving in terms of 
preferences that are by no means altogether reducible to biological 
needs and to the immediate situation. Human life is a moral life 
precisely because it is a social life. In human society co-operation and 
the other necessities of group living are not taken care of by instinct 
as they are for the social insects. There must be standards. 

The broad outlines of all ways of life are and have to be about the 
same because men always and everywhere are faced with certain un- 
avoidable problems which arise out of the situation "given" by na- 

15 Using a rating scale and a correlational technique of statistical analysis, these 
authors compare child-training practices and their relations to various customs 
and prevalent ideas of guilt and fear of others in 75 tribes. 



344 What Is Science? 

ture. Since most of the patterns of all cultures crystallize around the 
same points, there are significant respects in which each culture is not 
wholly isolated, self-contained and disparate but rather related to and 
comparable with all other cultures. 

Nor is the similarity between cultures limited to the fact that all 
cultures have marriage regulations, tools, music, graphic art, forms of 
shelter, ornaments, grammatical categories, and the like. There are at 
least some broad resemblances in content, and specifically in value 
content. Considering the exuberant variation of cultures in most 
respects, the circumstance that in some particulars almost identical 
values prevail throughout mankind is most arresting. No culture tol- 
erates indiscriminate lying, stealing, or violence within the group. 
The essential universality of the incest taboo is well known. No 
culture places a value upon suffering as an end in itself: as a means 
to the ends of the society (punishment, discipline, etc.), yes; as a 
means to the ends of the individual (purification, mystical exalta- 
tion, etc.), yes; but of and for itself, never. 

We know of no culture in either space or time, including Soviet 
Russia where the official ideology denies an afterlife, that does not 
ceremonialize the fact of death. Yet the more superficial conception 
of cultural relativity would suggest that at least one society would 
have adopted the simple expedient of disposing of corpses in the 
way most cultures do dispose of dead animals i.e., just throwing the 
body out far enough from habitations so that the odor is not trou- 
bling. When one first looks rather carefully at the astonishing variety 
of cultural detail over the world, one is tempted to conclude that 
individual human beings have tried almost everything that is physi- 
cally possible, and that nearly every individual practice has some- 
where at some time been institutionalized in some culture. To a 
considerable degree this generalization is valid but it is not com- 
pletely so. In spite of loose talk (based upon an uncritical accept- 
ance of an immature theory of cultural relativity) to the effect that 
definitions of mental disorder are completely relative to culture, the 
fact of the matter is that all cultures define as abnormal individuals 
who are permanently inaccessible to communication or who con- 
sistently fail to maintain some degree of control over their impulse 
life. Social life is impossible without communication, without some 



Anthropology 345 

measure of order: the behavior of any "normal" individual must be 
predictable with a certain range by his fellows and interpretable 
by them. 

To look freshly at values of the order just discussed is difficult 
because they are commonplaces. And yet it is precisely because they 
are commonplaces that they are interesting and important. Their 
vast theoretical significance rests on the fact that, despite all the 
influences that predispose toward cultural variation (biological vari- 
ability, differences in physical environments, and the processes of 
history), all of the very many different cultures known to us have 
converged upon these universals. It is perfectly true (and for certain 
types of enquiry important) that the value "thou shalt not kill thy 
fellow tribesman" is not concretely identical either in idea or feeling 
for an Australian aborigine and an American Indian. Nevertheless, 
the central conception is the same, and there is understanding be- 
tween representatives of different cultures as to the general intent of 
the prohibition. Some things are inevitable for all men; some habits 
are essential to survival and to a reasonably orderly life. 



The Tongues of Men 

There are perhaps only three kinds of activity in which normal adults 
in all groups take part about equally: sleeping, eating, and talking. 
Language has inevitably been of great interest to anthropologists, 
and they have studied it from many different angles. We all know 
from ordinary experience that a man's speech conveys a good deal 
of information about him: his level of education and good clues to 
the social class to which he belongs; often, the region in which he 
grew up; some hints as to his personality. Indeed, recent collabora- 
tion between anthropological linguists and psychiatrists suggests that 
the patient's speech and especially his intonation patterns may give 
the most sensitive and tangible basis for the diagnosis of certain men- 
tal disorders. 

Everyone also recognizes in a general sort of way that the language 
habits of a group are related to or reflect other group habits. The 
vocabulary of any people holds up a mirror to the rest of their 



346 What Is Science? 

culture, revealing what they have found it important to differentiate 
and name. The ancient Egyptians had no word for slave and no 
word for freedom. The political history of the English-speaking peo- 
ples has not given rise to such terms as putsch or coup d'ttat, and 
that is why we resort to a German and a French word when we have 
occasion to refer to events of this type. Even within closely related 
languages and cultures there are some interesting and suggestive 
differences. It may be significant, for instance, that the English 
"stand" for elections, while Americans "run/' Over and above vocab- 
ulary differences the presence or absence of words in one language 
which occur in another each language has a certain flavor that some- 
how expresses wider trends in the culture. Thus, a Japanese conversa- 
tion characteristically defines the relative status of the speakers with 
great precision but leaves quite ambiguous most of the remaining 
context. 16 

Once one goes beyond the superficial statement, anthropological 
linguistics gets immediately technical and a bit forbidding. This is a 
reflection of the fact that the methods of linguistics are the most 
distinctive of the behavioral sciences. In fact, linguistics most nearly 
resembles the physical sciences in rigor and elegance. In this brief 
section the best we can hope to do is to indicate three reasons for 

ta Because anthropological linguistics has become severely technical, it is now rather 
forbidding to other students of human behavior. This is a pity since nothing is 
more human than speech and nothing more revealing of a people's characteristic 
ways of behaving and thinking. Moreover, the use of language is the one major 
mode of behavior in which all "normal" adult members of the group participate 
about equally. Analysis of vocabulary reveals the principal emphases of a culture 
and also reflects culture history. The cliches of greeting and the bromides of daily 
small talk mirror standard social situations and often indicate the major tensions. 
Americans say "How are you getting on?"; Catholic Germans, "May God greet 
you"; Japanese, "There is respectful earliness." Swedish retains a form of the sec- 
ond personal pronoun "you" for use to inferiors, and lawsuits arise over who is 
entitled to use this to whom. Linguistic usages that grow up around differentiated 
terms used toward familiars, equals and superiors highlight the system of social 
stratification and of interpersonal relations generally. In France husband and wife 
normally address each other as "tu." But among the old aristocracy they call each 
other "vous," with the unexpressed understanding that the husband reserved "tu" 
for his mistress. French Catholics call God "vous," Protestants "tu." Everyone 
knows that schools, professions, cliques, criminal gangs and summer camps rapidly 
develop a special slang to symbolize their distinctiveness as a group. "The linguistic 
community" is a significant phrase. 



Anthropology 347 

believing that the anthropological study of language will be for the 
next generation or two in the vanguard of behavioral science. 

The first is the simple one that language is the sharpest model of 
culture generally. Language approaches pure culture: here one sees 
in complete clarity regular and patterned selection among a limited 
number of biological possibilities. Infants babble at random almost 
all the kinds of sounds found in known languages, but by the time 
they are a few years old they have learned to make and respond to 
the small number of sound types used in the speech of their elders. 
An adult finds it difficult, sometimes impossible, to reproduce ac- 
curately the sounds of a foreign tongue that he could have mimicked 
easily as a child. A Hindu confuses the English sound "t" in "top" 
with the "t" of "stop" not because he lacks the biological equipment 
to hear this distinction but only because this particular distinction has 
a different place in the sound system of languages deriving from 
Sanskrit. And this brings us to a second point where language is a 
nice paradigm of culture generally. As cultures have organization as 
well as content, so the sounds of any given language are not a 
congeries but an organized system. This comes out strikingly in the 
history of sound change. Once a new principle, say, stress accent or 
the contrast between voiced and voiceless consonants, is introduced 
into a language, the principle spreads to every set of similar sounds. 
What the Spanish linguists call "the empty boxes" get filled in so 
that symmetry throughout the system is preserved. 

Second, language is that aspect of culture where, thus far, order 
and predictability have been most successfully demonstrated. In the 
mid-nineteenth century Grimm's Laws (showing the regularity of 
sound shifts in Germanic and other Indo-European languages) were 
a dramatic answer to those who claimed that, however fixed in their 
courses the movements of the planets might be, human beings be- 
haved only according to the caprices of free will or the dictates of 
God. Since then there have been massive documentations of order- 
liness in linguistic change as well as some instances of sporadic 
change, analogous to the "mutations" known to genetics. In Latin 
between 450 and 350 B.C. the consonant "s" was changed to "r" 
-wherever it came between two vowels. For instances, genesos, the 
possessive of genus, became generis; meliosem ("better") became 



348 What Is Science? 

meliorem. The prediction, on the basis of analysis of sound systems, 
that ancient Indo-European had laryngeals 17 was confirmed a gener- 
ation later when Hittite records of 1500 B.C. were uncovered by 
archaeologists. Another prediction of 1877 about forms in early Greek 
was verified by an inscription found in 1913. During the eighteenth 
century in Hausa, an African language, "s" changed to "sh" whenever 
followed by one of four particular vowels. 

The study of sounds on a strictly scientific basis is now possible 
because linguists have discovered basic elemental units comparable 
to the atom in physics or to the gene in biology. Every sound system 
has a number of structure points called "phonemes." These 
are types or classes of sounds which are treated by the speakers of 
that language as a unit. Thus in English the sounds "p" in the words 
pin, spin, and nip which we English-speakers react to as if they were 
identical are, from the standpoint of an acoustic engineer, quite 
different. The English phoneme "p" makes up not a natural but a 
conventional or a cultural category. 18 Nature, as reflected in the sound 
waves recorded by the instruments of a physicist, here reveals three 
distinct sounds. But where the natural world presents nothing but 
an indefinite number of contingent varieties the intervention of 
cultural conventions creates a bundle of distinctive features that have 
a minimum sameness and are treated as a unit. In one language a 
sound that is made with the two lips, voiceless, strongly articulated, 
and with stopped breath is bundled together and contrasted with 
another sound that is otherwise identical but made with vibration of 
the vocal cords (voiced). In another language similar sounds are 

" Sounds produced with a deep simultaneous vibration of the larynx. Such sounds 
are occasionally made today by speakers of Indo-European languages but only as 
expressive features. 

18 A "phoneme" is technically defined as the class of all segments and spans con- 
taining given features. Take the English word "pin." There are three irreplaceable 
sound units here. Each occurs in other combinations: the first occurs, for instance, 
in pip, pill, pocket; the second in pip and pill but not in pocket; the third in tan, 
run and hen. But these three units cannot be further analyzed by partial resem- 
blances. In the case of "pin" the three phonemes are presented by three letters of 
our alphabet, but our conventions of writing are not always a trustworthy guide. 
In "thick" the first phoneme is represented by two letters "th," and the third 
phoneme by two more letters "ck." The linguist represents the first of these pho- 
nemes by a Greek letter, the second by simple "k." 



Anthropology 349 

contrasted not on the voiced-voiceless basis but on the force of 
articulation. The phonemic principle is a specific application of the 
cultural principle in general: one treats sounds in the conventional 
system within which they occur; one avoids imposing a pattern 
from without and seeks instead to discover that which is inherent 
within an historically derived organization. 

Linguistics with its discovery of ultimate significant entities 
(phonemes and their distinctive features) converges with modern 
physics which has revealed the granular structure of matter as com- 
posed of elementary particles. And in the last decade there has been 
exciting collaboration between the linguists and the communications 
engineers. The number of contrasts of distinctive features in the 
languages studied thus far run about six and eleven. The number of 
distinctive features needed to describe the number of phonemes 
would approach the minimum of Log 2 n, where "n" is the number of 
phonemes in the system. But the students of information theory 
pointed out that the communication needs of both speakers and 
hearers would enter into the picture and that therefore the actual 
number of distinctive features ought to be close to 50 per cent. In 
languages which have been analyzed this estimate has been roughly 
borne out. Moreover, in Spanish, where records at four time points 
have been studied, the number oscillates back and forth over this 
mean. 19 In other words, the balance between efficiency and redun- 
dancy is redressed. If the system gets out of line, the equilibrium is 
rather quickly restored. From these and other investigations we now 
know that the view of the older linguists that sound change was 
regular but "blind" (i.e., due purely to historical accident) is not 
altogether correct. Sound changes also tend to be "functional/' The 
way sounds are put together represents, among other things, a com- 
promise between the needs of the speaker and of the listener. 

Language has been described by the greatest of anthropological 
linguists 20 as "the mountainous and anonymous work of unconscious 
generations." These very aspects make the subject peculiarly acces- 

*For full information see Psycholinguistics (Memoir 10, International Journal of 
American Linguistics, 1954), especially p. 156 ff. 

w Edward Sapir, Professor of Anthropology and Linguistics at Yale until his death 
in 1939. See bibliogiaphy. 



350 What Is Science? 

sible to scientific study. For while the behavior of human objects of 
investigation is ordinarily modified by the investigation itself, linguis- 
tic behavior is largely unconscious and automatic and changes per- 
ceptibly through time only at a very slow rate. Moreover, linguis- 
tics also supplies possible runs of data through periods of time long 
enough to meet the demands of mathematical statistics. On Indo- 
European, Semitic, and Sino-Tibetan languages there are available 
statistical runs of four to five thousand years. The detailed record 
on such languages is truly "mountainous," and the most complete 
for any aspect of culture. 

The third reason for the central importance at this time of anthro- 
pological linguistics is the hypothesis that a language is the key 
which will unlock the structure of the total culture. One anthro- 
pologist, for instance, has asserted that there are remarkable similar- 
ities between the languages and the typical social organizations of 
the American Indians and between language and social organization 
in the Pacific Islands, the Far East, Negro Africa, and elsewhere. 
He claims too much on present evidence. Yet other anthropologists 
believe that there may be important resemblances between certain 
carefully delimited aspects of linguistic structure and certain carefully 
delimited aspects of kinship structure. A definitive answer to these 
questions will probably be obtained only after the very complicated 
data have been coded and fed into the giant calculating machines 
now in operation. 

Every language is undoubtedly a special way of looking at the 
world and interpreting experience. B. L. Whorf 21 has argued that 
concealed in each different grammar are a whole set of unconscious 
assumptions that channel perception and inference. Certainly any 
language is a logical relational system and not just a collection of 
words. Subject and predicate forms, contrary-to-fact conditions, tran- 
sitive and passive verbs, and the like, all imply a metaphysic. Logic is 
concerned with the patterning of certain cultural forms, and differ- 
ent languages are built upon different philosophical principles. West- 

11 One of the more interesting of recent American intellectuals. Trained in natural 
science at Massachusetts Institute of Technology, he earned his living as a top 
executive of the Hartford Fire Insurance Company but taught linguistics at Yale 
in his spare moments and published extensively in learned journals. His brothers 
arc Richard Whorf, the actor, and John Whorf, the water-colorist. 



Anthropology 351 

ern European languages make tense (the relation of before, present, 
and past) central in their verbs, whereas other languages make "as- 
pect" (the type of activity) crucial, and still others are primarily 
epistemological i.e., the verb must above all things state the kind 
of information on which the assertion is founded. 

Whorf pointed out that the language of the Hopi Indians gets 
along nicely without tenses. In the Hopi view time disappears and 
space is altered so that the Hopi do not conceive of the homogeneous 
and instantaneous timeless space of our supposed intuition or of 
classical Newtonian mechanics. 22 Whorf insists that various grand 
generalizations of the Western world, such as time, velocity, and 
matter, are not essential to the construction of a consistent picture of 
the universe. A Chinese scholar has suggested that the emphasis in 
the Chinese language upon "how" rather than "what" has led to the 
neglect of epistemology in China and little original development in 
science. A number of writers have related Western science to the 
nature of the Greek language and specifically to the facility for the 
creation of nouns in that language. 

The extent to which language is the shaper of ideas rather than 
merely a reproducing instrument for voicing them is an intensely 
arguable question but enormously interesting. Much experiment and 
other factual testing remain before we can say whether linguistic 
patterns inescapably limit sensory perceptions. Nevertheless language 

"To give concrete illustrations: in the Hopi Indian language one cannot use car- 
dinal numbers as imaginary plurals. One can speak of "ten men" because ten men 
can actually be seen together. One cannot speak of "ten days/' English "they 
stayed ten days" can be expressed in Hopi only as "they stayed until the eleventh 
day" or "they left after the tenth day." Actually, in this respect the Hopi language 
is more operational in expression. Likewise, in Hopi there are no nouns corre- 
sponding to English adverbs in grammatical form. Therefore one cannot objectify 
or personify the seasons as in English poetry. "Summer is hot," or "this summer" 
become in Hopi "summer is when heat occurs" and "summer now" or "summer 
recently." In the language spoken by the Trobriand Islanders of Melanesia causa- 
tion cannot be expressed only propinquity in time or space. In selecting verbs 
in Western European languages we must refer to past, present or future (and to 
varying combinations of these basic notions). Other languages which dispense 
with tenses are fussy in insisting that each verb form must indicate whether the 
information in the assertion is derived from direct sense observation, from infer- 
ence on the basis of sense experience, from a myth, from hearsay, from knowl- 
edge of habitual or customary behavior on the part of an individual or a group. 



352 What Is Science? 

does at least influence how we talk about what we perceive: how we 
categorize our perceptions and reason from them. Language is both a 
key and a fetter to thought. At present it appears that different 
languages have some influence upon the thought processes of their 
speakers, but that language both determines and is determined by 
the total experience of the people who use it. 



The Uses of Anthropology 

The direct practical bearing of archaeology and of historical anthro- 
pology generally is limited. One could point to the role of archaeol- 
ogy in public adult education through popular articles and through 
the participation of archaeologists on the staffs of our museums and 
national parks and monuments. The historical study of human evolu- 
tion is useful to physicians and dentists because the evolutionary 
history of limbs, jaws and teeth makes clear certain causal elements in 
present difficulties. However, the main contribution of historical an- 
thropology is indirect. To the trained eye the past gleams beneath 
the surface of the present. The business of the anthropological histo- 
rians is to reveal the less obvious features hidden from careless eyes 
in the contemporary situation. Anthropological history, because it is 
comparative, serves better than does the history of any single people 
or period to give enlightening perspective. Only in this light can we 
hope to understand the vast processes of world history: the relative 
importance of invention and discovery as opposed to copying and to 
the spread of new things; the limitations and stimulations imposed 
by the natural environment; comparison of the significance of out- 
standing individuals contrasted with massive but impersonal histor- 
ical trends; the whole problem of the growth, flourishing and decay 
of civilizations. 

Anthropological linguistics is applied more immediately. The 
methods now used by the United States government to teach mili- 
tary and civilian personnel to speak languages of non-Western type 
are largely the product of the experiences of anthropologists in their 
field work. Linguistic analysis has served in the deciphering of 



Anthropology 353 

secret codes. The study of exotic languages has had important im- 
plications for modern logic and for taking account of the extent to 
which Western science is bound by the nature of Western lan- 
guages. All grammars are ways of classifying relations between things 
and events. Relationships that are paid attention to in all languages 
may be presumed to constitute the subject matter of universal logic: 
the logical problems that are inevitably posed to human beings by 
virtue of the nature of their nervous systems and their situation in 
the physical world. Conversely, an unfamiliar category in a primitive 
language may suggest a logical problem heretofore neglected by the 
logicians of Western civilization. 

Physical anthropology has many technical, though intellectually 
trivial, applications, most of which arise from the careful studies 
made by physical anthropologists of the size and shape of the human 
animal: the utilization of anthropologists in the identification of war 
dead; in the design of railway seats, gas masks, seating and seat-desk 
arrangements designed for growing school children, gadgets adapted 
to body size and capacity in aviation and in industry, and other 
equipment; in the systematic planning of the sizing of clothing for 
the armed forces and for mass commercial manufacturers. More in- 
teresting scientifically are the contributions of physical anthropology 
to medicine and to dentistry. Growth studies of the bones and of the 
development of posture and investigations of the evolutionary as- 
pects of postural adaptatation have been useful to orthopedic sur- 
geons even to the extent of improving the quality of artificial limbs. 
Growth studies, particularly those having to do with "racial" and 
environmental conditioning factors, have aided pediatrics. Extended 
knowledge of the range of variation in human pigmentation and of 
the "racial" response to radiation has contributed to dermatology. 
Obstetricians have been helped by information on female pelvic 
types, growth changes in the pelvic bones, sex differences, and long 
series of comparative pelvic measurements. Constitutional anthropol- 
ogy has aided in selecting personnel and in establishing performance 
standards in aviation and other aspects of military medicine. Evolu- 
tionary and growth studies of the teeth and jaws have contributed 
to the ability of dentists to treat and prevent malformations of the 



354 What Is Science? 

jaws and teeth. Analyses of dental variability among "races" and 
among groups having different diet and tooth-use patterns have 
added to the science of dental medicine. 

The practical side of cultural anthropology has many facets. In 
part, as in the case of physical anthropology, they are primarily 
technical. Anthropologists act as information gatherers and "trouble 
shooters" in the problems of administering and generally dealing with 
colonial, minority or dependent peoples. To illustrate: an American 
Indian tribe that was poverty stricken further complicated its eco- 
nomic problems by destroying the dwelling and all the personal prop- 
erty of a deceased person. An anthropologist persuaded them to cease 
this practice by suggesting an extension of "fumigation" procedures al- 
ready established in their religion. The objective advocated by U. S. 
government officials was achieved, but achieved within the frame- 
work of the native culture. The British were having serious trouble 
with a people on the West Coast of Africa. It took an anthropologist 
to point out that the uprisings occurred because some British were 
taking back to England as "curios" certain wooden stools which the 
Ashanti regarded as embodying the guardian spirits of their people. 

Often the primary role of the anthropologist is that of a "go- 
between." He interprets the people of different culture to the ad- 
ministrators and, in turn, interprets the administrators to the ad- 
ministered, thus improving communication and minimizing needless 
friction. One of the great lessons of applied anthropology thus far is 
that no amount of knowledge of the culture of one group will take 
us very far. There must be an equally technical analysis of the other 
group involved in the interaction. To get along with the French we 
must understand ourselves as well as the French. 

Industrial anthropology has been mentioned. The applications of 
cultural anthropology in medicine are expanding rapidly. Anthro- 
pologists study the social structure of hospitals (doctors, nurses, or- 
derlies, patients and visitors) with somewhat the same methods that 
they have developed in work with primitive tribes. Cultural and sub- 
cultural factors in disease susceptibility and in doctor-patient rela- 
tionships are investigated. The largest number of anthropologists em- 
ployed outside the world of colleges and museums is, however, in the 
government and in international agencies. First and foremost, these 



Anthropology 355 

anthropologists work as area specialists in intelligence, psychological 
warfare, and communications groups. Effective communication of 
any kind with foreign groups requires a systematic analysis of their 
way of life, of their habitual, taken-for-granted manner of feeling, 
thinking and reacting. It also requires something more than a "com- 
mon sense" understanding of how human beings generally leam, or 
are changed, through communication. 

A generation hence educated citizens are likely to accept the fact 
that there is a science of human behavior. They will assume that 
anthropology must play a part, along with the other sciences and with 
economics and history, in the field of international relations. Anthro- 
pological field work has already established that the objective superi- 
ority of a technological process or a food or a public health practice 
does not automatically win its acceptance abroad. The implications 
for the Point IV program, medical and other projects of foundations 
and religious groups are obvious. 

At present, however, there is not uniform enthusiasm for the turn- 
ing of anthropology from the natives toward international relations, 
industry and the study of American and "modern" cultures gener- 
ally. Enthusiasts for this development feel that only a science which 
sees institutions and values in cross-cultural perspective can usefully 
be applied to the problems of the mid-twentieth century. Those who 
are troubled by anthropology's new look doubt the applicability of 
anthropological field methods to complex, dynamic modern civiliza- 
tions; they question the relevance of principles derived for the most 
part from the examination of small, "static" societies. 

As usual, there is much to be said on both sides. Some anthro- 
pologists are undoubtedly moving a little hastily into the contempo- 
rary field. They are insufficiently critical of their discipline and of 
their own work. One can point to a few irresponsible pronouncements 
suggesting that anthropology has the answer rather than a useful but 
partial and limited contribution to some contemporary problems. 
There are quarters in Washington and even in the business world 
where anthropology is oversold, where in effect it is regarded as the 
newer magic, where anthropologists are being asked questions which 
the present generation cannot hope to answer. To the extent that 
anthropologists encourage or even countenance such overestimation, 



356 What Is Science? 

the profession will pay. The present demand for consultants and for 
workers on research of immediate relevance threatens the normal 
structure of the profession. Too many young men are going immedi- 
ately into the applied field without the seasoning of further field 
work, teaching and reading. Too many older men "consult" so much 
that they fail to keep up their basic research. There is no doubt that 
the detachment upon which anthropologists, rightly or wrongly, have 
prided themselves, is challenged. 

On the other hand, the great bulk of anthropological publication 
remains descriptive, detailed, rigorous within the limits of the ac- 
cepted theoretical framework. Against the few messianically tinged 
books of too easy generalization that have caught the public eye, one 
can name hundreds of solid monographs produced in the same time- 
period. Perhaps it is also fair to ask whether the same standards of 
criticism have been applied to these works as to comparable popular 
books from other fields. When the anthropologist writes of Yap or of 
Dahomey, he may be found tiresomely esoteric or idly amusing, but at 
any rate he is safe. When he writes of American social classes or of 
sexual behavior or of Soviet-American relations, he can no longer be 
ignored or reserved for cocktail-party talk. He should, to be sure, be 
held to the level of workmanship that he presumably adhered to in 
describing Yap, or at least required to avow publicly the thinness of 
his data. Yet there are grounds for suspecting that the emotional 
heat of many critiques was generated less by righteous indignation at 
careless scholarship and logic than by fury against the raising of cer- 
tain personal and cultural issues comfortably buried in the uncon- 
scious. One must also, I think, make careful discount for polemics 
engendered by the rivalries of vested interest. Some sociologists do 
not like anthropological poachers at all. Some literary people feel 
that the depiction (other than that made possible with the aid of 
brass instruments) of the ebb and flow of human feeling in the social 
scene is the inalienable property of the novelist and the poet. 

One of the war cries of the Thomases who doubt modern 
anthropology is the relative lack of numbers, of tables showing ranges 
of variation, of statistical manipulations. In part, this dissatisfaction is 
justified. Cultural anthropologists have often been cavalier on the 
problems of representativeness and of validation. In part, however, 



Anthropology 357 

these objections arise from a misunderstanding of the nature of 
"proof" in the cultural realm. What is significant in cultural phenom- 
ena is often not distance or intensity or other measurable quanti- 
ties, but rather position in a pattern under a given set of conditions. 
The pertinent variation is alternation from one configuration to an- 
other, rather than movement in terms of measurable positions. 

In the present-day world the constancies and variations between 
peoples, and the reasons for them, are a matter of the most intense 
practical as well as intellectual interest. Yet anthropological knowl- 
edge and the anthropological viewpoint can be disturbing. They 
seem to open the way to a complete and chaotic relativism. This 
interpretation is not warranted by the empirical data of anthropology, 
but it must be admitted that anthropologists have insufficiently em- 
phasized the order and similarities in human cultures. In part, resist- 
ance to anthropology is an aspect of a much wider process: a fear of 
the freedom of the open society, a frightened retreat from the frus- 
trating heterogeneity of the twentieth century. 

Anthropology is also sometimes reproached by philosophers, the- 
ologians and moralists for exalting the irrational and nonrational 
aspects of human conduct. It is true that anthropology grants to the 
varieties of human custom the same kind of amnesty which the psy- 
chiatrist gives to erotic dreams. But no moral judgments are involved. 
Rather, these phenomena are deemed to have meaning and hence to 
be worth study. Anthropology, however, has never been "vitalist" in 
tone, advocating a surrender to the forces of chaos and unreason. On 
the contrary, like all sciences, anthropology is the study of discover- 
able regularities; it seeks to extend the areas which reason can under- 
stand and perhaps to some extent control. In the contemporary 
world where varied races and cultures are in uncomfortably close 
contact, it is a primary intellectual function of anthropology to sup- 
ply, on a smaller scale and in a scientific manner, the perspective 
which philosophy has traditionally attempted to give us in a cosmic 
and unscientific manner. 



PSYCHOANALYSIS 



ERICH FROMM 



about 

Erich Fromm 



Erich Fromm was born in Frankfurt, Germany, in 1900. After study- 
ing sociology, psychology and philosophy at the University of Frank- 
furt, he proceeded to Heidelberg where he got his doctorate in phi- 
losophy in 1922. He continued his studies at the University of 
Munich and it was in this city that he was first trained as a psycho- 
analyst. Further training followed at Frankfurt and at the Berlin Psy- 
choanalytic Institute, from which he graduated in 1931. The same 
year saw the publication of his first book, The Evolution of the 
Dogma of Christ. 

Fromm s career as a lecturer began in the period 1 929-1 932 
when he gave courses at the Psychoanalytic Institute in Frankfurt 
and at the Institute for Social Research at Frankfurt University. In 
1934 he came to the United States and has since lectured at Columbia 
University, Yale, the New School of Social Research, Bennington 
College and the William Alanson White Institute of Psychiatry, 
where he also served as Chairman of Faculty. Since 1951 Dr. Fromm 
has spent part of each year in Mexico, holding a professorship at the 
National University and training psychiatrists in psychoanalysis. 

Fromm has been brilliantly successful at attracting large audiences 
for the most pressing issues of psychology, psychiatry and sociology. 
His books include Escape from Freedom, published in 1941; Man 
for Himself, 1947; Psychoanalysis and Religion, 1950; and The For- 
gotten Language, 1951. One of his main themes is the effect of 

360 



about Erich Fromm 361 

modern social and political circumstances upon the individual. In 
Escape from Freedom, for example, he portrayed with unusual sen- 
sitivity what it is within man that not only permits him to tolerate, 
but even causes him to welcome, the yoke of authoritarianism. Man 
for Himself examines the psychological basis of ethics, how mans 
nature shapes his moral beliefs and values. The forces in Western in- 
dustrial society that lead to mental illness and how these forces can 
be counteracted is the subject of Fromm s The Sane Society, pub- 
lished in 1955. In the following essay he explains with admirable 
clarity the fundamental ideas of psychoanalysis and their develop- 
ment in theory and practice by various schools since Freud. 



PSYCHOANALYSIS 

ERICH FROMM 



Medieval culture was a system based on traditional beliefs, in which 
the world seemed closed and hence certain and secure. The earth, 
and man on her, were the center of the universe. Everything was 
ordered by the laws of God, which had been revealed to man. There 
seemed to be nothing new to discover, no blank space to fill in. But 
about 1500 this secure and closed world burst wide open. Man was 
thrown out of his central place from which the whole universe seemed 
well ordered and known. Everything around him, and he himself, 
became a problem, a question, something to be discovered. The first 
crack in the shell of serenity was Copernicus' discovery that the sun 
is the center of our planetary system. This has led to a knowledge of 
the skies in which the sun is only one amongst billions of suns, in a 
galaxy which is but one amongst billions of galaxies. Copernicus be- 
gan a train of insights which culminated 500 years later in the theo- 
ries of Einstein and others as to the nature of space, energy and 
matter. Not only do our senses deceive us about the relative posi- 
tion of sun and earth, they deceive us even more thoroughly so 
contemporary physicists teach us about the physical environment 
which surrounds and supports us. 

The new discoveries about nature began earlier, and went further, 
than those about man, but the latter followed the same principle of 
trying to arrive at the forces behind observable phenomena in the 
fields of man's biological, social and psychological development. 

362 



Psychoanalysis 363 

In essence, this new principle was that not sensory experience nor 
common sense nor tradition is a guarantee of the truth; that to grasp 
reality outside of man and within him we must know the nature 
and direction of forces which are not directly visible, but which can 
be inferred from the visible phenomena they produce. Darwin hurt 
man's vanity by showing how he had developed, under a law of natu- 
ral selection, from distant animal origins. Marx showed that man's 
social systems, and even his thought and culture, are determined by 
social forces which operate behind his back, as it were. Freud com- 
pleted the process by showing that the conscious thoughts man has 
about himself and others are only a small part of what goes on within 
him. What is more important, he showed that most of the acknowl- 
edged thoughts are products of fears and desires which are not ac- 
knowledged. Freud taught man to be objective and to be humble; to 
be skeptical toward his conscious thoughts; to probe for the truth 
hidden in his unconscious, rather than to be satisfied with what he 
consciously believes to be true. Freud's discoveries are part and parcel 
of the progress made toward objective thought in the last 500 years, 
toward seeing the world, nature, our fellow men and ourselves as 
they are, not as we want them to be. 

Psychoanalysis is a psychological theory, as well as a method of 
therapy, for mental disturbances (psychoneuroses). Although the 
theory and the therapy are closely related, they must be dealt with 
separately, because, if for no other reason, the theory is important to 
any student of human nature, while the therapy is of great concern 
only to those who train themselves to cure mental sickness or to those 
who suffer from it. 

Nineteenth-century psychology was mainly occupied with describ- 
ing and classifying various processes in the conscious mind (percep- 
tion, memory, etc.). Freud broke from this pattern by setting himself 
the goal of answering questions which until then had been dealt with 
mainly by philosophers and novelists: what makes man act, think 
and feel as he does? What are the forces underlying and determining 
his behavior? What law can be observed in the operation of the 
human mind? 



364 What Is Science? 

1. Psychoanalytic Theory 

The fundamental discovery of Freud a discovery which will prob- 
ably influence thought about man as Copernicus' discovery continues 
to influence man's thought about the universe is his concept of 
the unconscious. Although Spinoza, almost 300 years earlier, had 
stated that we know our desires, but do not know the reasons for our 
desires (and hence live under the illusion of choosing freely), Freud 
succeeded in showing more widely and more concretely what the 
statement implied. He demonstrated that none of us is aware of 
more than a small sector of our mental personality (the conscious) 
while the bulk of what goes on within us evades our awareness, is un- 
conscious, repressed. 

Two simple examples may help to clarify the point. A man who is 
constantly bragging, boasting, belittling others is perhaps aware of 
himself as a masterful, superior person. What he is not aware of is 
that in reality all these feelings of power and superiority are only com- 
pensations for the very opposite. Deep down he feels weak, helpless, 
childish, and at the very moment when he tells us "look here what a 
great guy I am," he is really praying "do not let them find out that I 
feel like a helpless child." If we were to investigate further, we might 
find that this man feels like a helpless child because he has never 
overcome a deep fixation to his mother, a passive attachment which, 
normal for the child, is weakening for the man and should long 
since have been severed. His aim is probably still to be nursed, 
cared for, protected, admired by mother, and just because of his at- 
tachment, he feels like a child and hence weak and inferior. He may, 
in a more extreme case, have acquired the habit of compulsive 
drinking; only when under the influence of liquor can he overcome 
the feeling of powerlessness and at the same time the drinking is a 
substitute for his wish to be nursed and indulged by mother. The 
deeper one searches into the unconscious, the more links one un- 
covers in the chain of behavior. 

In the other example of unconscious motivation a young student, 
brilliant, intelligent, conscientious, gets so frightened before an ex- 
amination that he is almost paralyzed and jeopardizes his whole ca- 



Psychoanalysis 365 

reer. He is particularly frightened when the examiner is a teacher 
whom he does not like. Otherwise, the young man shows no signs of 
fear, has no feeling of inferiority, and is always poised and sure of 
himself in his relationship to older people or contemporaries. If 
one seeks the reasons of his examination fear, one finds at first an in- 
tense rage against the examiners, and especially the ones whom he 
does not like. Behind that rage is a feeling that it is an unbearable 
humiliation that he should be forced to submit to authorities who 
can decide about his career. Without going into the history of this in- 
tense rebelliousness against authority, it may be said that his anxiety, 
of which he was conscious, replaced and covered up what he was 
not aware of a deadly rage which he had to repress because to show 
and express it would have made his position untenable. Here, as in 
the first example, a person is aware of his feeling, but not aware of 
what causes it. Freud compares the relationship between the con- 
scious and the unconscious to an iceberg: the small part of it which is 
visible is the conscious; the bulk of it, which is submerged beneath 
the water, is the unconscious. He proved empirically the truth and 
significance of an earlier statement by Nietzsche: " 'I did that/ says 
my memory. 'I could not have done that/ says my pride, and remains 
inexorable. Eventually the memory yields/' 

Closely related to the concept of the unconscious is the concept 
of resistance. We do not want to know that which we have repressed, 
because it conflicts too much with our own ideals and standards, 
with the picture which we have, or which we want others to have, of 
ourselves. We do everything to make sure that what is repressed does 
not come to light. We deny it, we get angry with someone who 
touches upon it, we get tired and sleepy when mention is made of it, 
or we hide it by rationalizations. 

The concept of rationalization is one of the most important dis- 
coveries in Freud's theoretical system. All of us rationalize when we 
attempt to justify an action, thought or feeling as motivated by 
reason, conscience, practical necessity, instead of admitting that it is 
motivated by irrational desires. The process of rationalization is well 
known to anyone who ever tried to quit smoking. In order to explain 
to himself why he wants to smoke just that one cigarette, he dis- 
covers that it is because he feels so good, or because he feels so bad, or 



366 What Is Science? 

because everyone else is smoking, or that he is not so weak as to have 
to give up smoking, or that there are so few pleasures in life otherwise, 
or ... or. ... There is hardly an end to the number of ra- 
tionalizations in this, as in so many other similar situations in life. 

To give one more illustration, it is the rationalizaton of a destruc- 
tive or sadistic person that he beats his children, or tells people pain- 
ful and hurtful things, in plain response to duty. He sees himself 
obedient to noble impulses, when in reality he is driven by the desire 
to hurt or to destroy. 

The unconscious, operating thus in the dark, is not immediately 
accessible to conscious investigation. We have to infer it from ac- 
cumulated data, as the theoretical physicist often infers forces which 
in themselves cannot be observed directly. However, in certain situa- 
tions unconscious forces can be observed directly. These situations 
are all alike in that they are states of dissociation, ones in which the 
conscious mind is not active, or not properly functioning. The only 
normal state in which this dissociation occurs is sleep. Sleeping, we 
shed our consciousness and withdraw our watchful attention from 
the outside world. In this condition, we think and feel things which 
are quite contrary to our conscious, daytime thoughts. Somebody, 
for instance, may have hurt our feelings during the daytime, but we 
may not have been aware of feeling hurt, much less of feeling angry. 
The following night, however, we may dream that the person who 
had hurt us committed a crime, was caught by the police, and has 
been executed. 

In most cultures dreams have been taken seriously as meaningful 
expressions of our mind. But by the time of Freud, this attitude had 
generally changed in Europe, and dreams were believed to be silly 
and meaningless phenomena. One of Freud's greatest achievements 
was to show that dreams express feelings and ideas which we dare 
not be aware of in waking life, sometimes with utter frankness, but 
most of the time hidden and distorted even in the privacy of our 
sleep life. Freud assumed that dreams are always the fulfillment of 
unconscious wishes which we do not dare to recognize in waking life. 
(This author, like some others, believes that dreams are not always 
or necessarily expressions of inadmissible desires; that often we are 
more wise, more human, more decent when we are alone with our- 



Psychoanalysis 367 

selves in the state of sleep than we appear to be in the market place 
of daily living.) 

Another state of dissociation in which the unconscious can be ob- 
served directly is hypnosis. In a state of deep trance, a grown-up per- 
son may feel and act like a child of ten, five or two, provided the 
appropriate suggestion is given to him. This experiment of "age re- 
gression" shows that all previous stages of our life are still alive within 
us; that in the specific condition of hypnotic trance they again take 
hold of our feelings, only to be completely forgotten when we re- 
turn to daylight thinking. Many other experiments with hypnosis give 
a striking proof that the unconscious is pursuing its hidden course 
"behind the back" of consciousness. Thus, for example, Dr. Mitchell 
Gold * in his studies on hypnosis showed how emotional responses are 
elicited by specific factors or constellations in the environment. The 
subject, under hypnosis, is told that she is accused of something and 
that she feels anxious and guilty; at the same time, the hypnotist 
shows her his raised finger. At the mention of being accused, the 
subject shows all signs of terror and anxiety, which leave her when 
she is assured that the accusation was false. After three or four repeti- 
tions of this little drama, she reacts with the same signs of terror 
when only the finger is raised, no mention being made of an accusa- 
tion. In other words, a conditioned reflex has been established and 
the raised finger, which was at first neutral, became a conditioned 
stimulus. After she has emerged from the hypnotic trance, and is 
aware of nothing that has taken place, she refuses to look at the 
hypnotist's raised finger, and turns her head away until the finger is 
lowered. In her unconscious she is still afraid of the accusation, sym- 
bolized by the finger, and yet, consciously, all she feels is an inex- 
plicable aversion to the finger. 

In cases of insanity, ideas and feelings which are repressed in a 
normal person are accepted as real. The paranoid person may be con- 
vinced that people are plotting against him, or he may be convinced 
that he is a Roman emperor. Similar suspicions or grandiose ideas 
would be repressed by the nonpsychotic individual and he might be 
aware of no more than a magniloquent daydream or a nagging anxi- 
ety that people do not like him. His thinking is controlled by an 
1 Research Supervisor of the Scientific Personality Research Corp., New York. 



368 What Is Science? 

awareness of reality, and the irrational phantasies can never appear 
to him as if they were real. To the psychotic person reality appears as 
it appears to all of us when we are asleep. We give up most of our 
reality awareness in sleep and do not doubt the reality of our dream 
experience. But when we wake, the unreality of the dream strikes us 
so forcefully that we often cannot even remember its content. Dreams 
are transitory states of insanity, or insanity may be said to be dream- 
ing while being awake. 

Another situation in which unconscious feelings are expressed 
directly is the state of mind caused by various drugs, the most fre- 
quent being intoxication by alcohol. The drunken person has sus- 
pended most of his critical judgment, and when he transforms him- 
self into a boastful megalomaniac, or into an aggressive attacker, he 
gives himself over to forces so repressed in his sober state that he 
may have no hint of their existence. 

The theoretical as well as the practical problem which confronted 
Freud was to find a way in which a person who is neither psychotic, 
drunk nor asleep could discover what was in him, yet outside his 
awareness. To become conscious of what is unconscious seems a 
paradox; it was part of Freud's genius that he solved the riddle. He 
began by using hypnotic methods, but gave these up after a while in 
favor of the study of dreams the "royal road to the unconscious" 
and of a method he called free association. On the face of it, this 
latter process is simple. A person is told to say just what comes to his 
mind, disregarding all conventional rules of what is proper, intelli- 
gent, polite, etc. The psychologically trained listener can discover in 
these random associations connections of which the subject is not 
aware. He may thus detect thoughts and feelings which are uncon- 
scious. A simple example will illustrate the point: thought (a) deals 
with a friend toward whom the patient feels consciously very friendly, 
although in fact he felt jealous on hearing the night before of his 
friend's promotion; association (b), apparently without connection, 
deals with an incident the patient read about in the morning's paper: 
a man was killed by a rival; association (c) recalls the patient's life 
in school, when he felt very unhappy at having been demoted from 
first to second place. Though the patient is not consciously aware of 
a connection among these three associations, it is not difficult for an 



Psychoanalysis 369 

objective observer to find the thread. As in the dream, the repressed 
material of free association is often censored and distorted. At the 
point when the free association might bring out significant repressed 
material, the patient may begin to talk about trivial things, feel 
sleepy, get discouraged, angry or what not. He does not realize that 
all these reactions are so many attempts to get away from the re- 
pressed material. 

In addition to dream interpretation and free association, Freud 
discovered a third method for getting a glimpse of unconscious striv- 
ings; this was the study of transference. Freud noticed that his pa- 
tients often developed ideas about him and reactions to him which 
were not founded at all on reality. One patient might see him as an 
all-powerful or all-wise man; another as a weak and timid man; a 
third as a sinister ogre. As in the states of dissociation mentioned 
above, these feelings were experienced as being quite real, and it was 
difficult for the patient to convince himself that they were not. Fur- 
ther study showed that these particular feelings were not accidental; 
that the patient had had similar experiences with a significant person 
of his early childhood father, mother, brother, etc.; that uncon- 
sciously he was still experiencing other people in terms of these early 
feelings, seeing them, not objectively, but as if they were those same 
important childhood figures. He transferred his experience, as it were, 
from the past to the present. 

This concept of transference cannot be understood without refer- 
ence to another of Freud's discoveries: the importance of the first 
years of childhood, especially the relationships with parents and sib- 
lings, on the character development of the child. While Freud never 
thought that the newborn child is like a blank sheet of paper on 
which the environment simply writes its text, and while he was con- 
vinced that each child is born with certain constitutionally given 
qualities, he nevertheless could show the tremendous influence of 
early childhood experiences on all later development. The phenome- 
non of transference demonstrated that the adult retains the experi- 
ences of early childhood, often to such an extent that he is not able 
to see the world objectively. 

So far I have given a brief summary of the most important of 
Freud's findings which are accepted by all psychoanalytic theories 



370 What Is Science? 

based on Freud's discoveries. However, there is a great deal of con- 
troversy about the content of what is so strongly repressed and so in- 
fluential in man's life. Freud himself believed that the most powerful 
and most repressed strivings are sexual (the energy of the sexual drive 
he called "libido" ) . He assumed that from birth on the individual is 
endowed with sexual strivings, but that the nature of the strivings 
undergoes a definite development from birth until puberty. At birth 
the libido is mainly centered around the mouth, and its aim is to be 
nursed. Later, the passive wish to be nursed is transformed into the 
more active drive to bite, and to possess with the mouth. The stage 
after this "oral libido" is the "anal libido," connected with the func- 
tions of elimination and resulting in various psychic tendencies like 
parsimony, overcleanliness, overorderliness (or their opposites). After 
this, the libido for the first time centers upon the genitals, and pleas- 
ure is connected with genital excitement. Following this stage, which 
occurs around the age of five or six, Freud assumed the existence of a 
so-called "latency period," which lasts until puberty, and during 
which no further change occurs in sexual development. With puberty 
the libido gains its full development and seeks its satisfaction nor- 
mally in the sexual union with a member of the other sex. 

This development, according to Freud, is not as simple and easy 
as it may sound. The main complication is that, when the phallic 
level has been reached, the little boy becomes closely attached to his 
mother, but at the same time finds himself confronted by his father, 
an invincible rival who forces him to resign, and eventually to 
suppress, his sexual wishes. (Little girls experience a parallel develop- 
ment.) Under the name of the "Oedipus complex," Freud described 
the development in which the little boy hates his father, but then be- 
comes afraid of him and, instead of hating him, identifies himself 
with the father. Freud believed that in a normal development the 
incestuous attachment to the mother is overcome, while in all cases of 
mental sickness the unsolved Oedipus complex is the center of the 
pathological picture. 

Freud attempted to explain character trends in terms of his libido 
theory. To him, the forces which we find underlying a person's char- 
acter are in the last analysis sublimations of, or reaction formations 
against, the libidinous strivings, especially the pregenital ones. Thus, 



Psychoanalysis 371 

Freud assumed that a dependent, receptive person was stalled, as it 
were, on the oral-receptive level of libido development; an aggressive, 
exploitative person, on the oral-sadistic level; a stingy, overorderly, 
pedantic person, on the anal level of libido development. 

In spite of a certain dogmatism, Freud was never a man to be 
easily satisfied by his own theories, nor one to shut himself off from 
new observations of facts. Perhaps the First World War brought to a 
climax Freud's awareness that he had not paid sufficient attention to 
the role of destructiveness and hostility among the motivations 
within man. Until then he had thought that hostility was a sec- 
ondary factor, a reaction to sexual jealousy and rivalry; now he 
began to believe that it had a much deeper source. The development 
of his idea led him eventually to assume that there was in man an 
innate drive for destruction which was just as powerful as eros. Even- 
tually he saw in the sexual instinct one manifestation of a drive for 
life, the aim of which is to unite living matter, while he saw in 
destructiveness and hostility one manifestation of the drive for death, 
the aim of which is to return to the original state of inorganic 
matter. Thus sexual desire and hostility became only the two most 
visible expressions of the two forces battling within man, one di- 
rected toward life, the other toward death. In this theory Freud 
attempted to connect psychoanalysis wifh general biological and 
philosophical concepts, and thus laid the foundation for the more 
philosophical treatment of psychoanalytic data. 

Freud applied his theoretical concepts not only to the individual, 
but also to the study of society and culture. He believed that primi- 
tive man lived out his instinctual desires without too much frustra- 
tion by society, but that because of this there was a great deal of 
mutual hostility, and thus a great deal of insecurity, in life. Progress 
in civilization was essentially an increasing repression of man's in- 
stinctual desires. These repressions resulted in sublimation, that is, 
the transformation of the libido into culturally valuable aims which 
have no direct connection with the original instinctual aims. Culture, 
according to Freud, is thus an effect of sublimation. But many people 
lack the capacity for sublimation which is required by the rigid rules 
and taboos of many societies; the conflict between their instinctual 
forces and the social requirements for repression produces neuroses. 



372 What Is Science? 

Freud's theory on the development of culture is accordingly rather 
pessimistic. The more man develops culturally, the more he must 
frustrate his instinctual desires, and as his civilization increases, so 
does his proneness to mental sickness. 

According to his libido theory, Freud assumes that religion, art, 
philosophy, political systems and so on, are all outcomes in one 
way or another of libidinal forces, and unsolved libidinal conflicts. 
He thus becomes a critic of religion, in which he sees mainly the ex- 
pression of the child's dependence on an all-powerful father. Never- 
theless, it would be quite wrong to assume that ethical ideals play 
only a minor role in Freud's concepts; like the philosophical leaders 
of the eighteenth century enlightenment period, he believes in truth 
and freedom as the aims toward which man must strive for a satis- 
factory solution to life. 

It was almost unavoidable that Freud's theories would make him 
into a social critic (or perhaps only a social critic could have arrived 
at such theories). While he was convinced that a certain amount 
of sexual repression was necessary for the development of culture, he 
protested against the degree of repression which was characteristic of 
the nineteenth century. He believed that the strictness of the moral 
code of the Victorian age went beyond its legitimate cultural func- 
tion and created more neurosis and mental suffering than was war- 
ranted. He also saw that the degree of sexual repression customary 
in his culture tended to cripple the free development of man, and to 
hobble his reason, thus preventing him from emerging from the state 
of childhood to that of maturity. 

But in spite of the fact that Freud was a social critic, and in many 
ways a spiritual companion of the enlightenment philosophers of the 
eighteenth century, he was very different from them in his pessimism 
about the future of man. Since he did not see the destructiveness 
of man as a trait produced by the cultural and social conditions of 
his age, but as an innate trait, he assumed that no social or spiritual 
change could eradicate it: thus, wars and civil wars, suicide and 
murder, are inevitable. Man to him was competitive and hostile by 
nature, and resembled the being characterized by Hobbes in the 
words: Homo homini lupus. The position was not too different from 
that of the classical economists who saw competitiveness-aggressive- 



Psychoanalysis 373 

ness as elements of human nature, rather than as traits produced by 
the social order in which they lived. 



2. Psychoanalytic Therapy 

Psychoanalysis as a therapy is an application of its theory to the prob- 
lems of mental sickness. It must not be thought from this, however, 
that Freud first developed his theory, and then applied it. The the- 
ory itself developed from his treatment of mentally sick patients, and 
theory and practice constantly complemented each other. In the first 
years of psychoanalytic therapy, the patients who came to Freud or 
other psychoanalysts, mostly suffered from definite neurotic symp- 
toms, such as inordinate anxiety, morbid fears, psychosomatic reac- 
tions to certain purely psychic stimuli, or obsessive and compulsive 
thoughts and rituals. Freud assumed that the symptoms resulted from 
"the injuring of the instinctual impulses through repression," that 
they were an indication of, and substitution for, an unachieved in- 
stinctual gratification. In order to cure a symptom, the patient must 
become aware of the unconscious instinctual wishes. Being aware of 
them, he can then find a more mature and effective solution to the 
conflict between instinct and the organized and conscious part of the 
self or the id and the ego as he called these two than the one 
found in the formation of the symptom. 

In the course of the years, the type of patients who came for psy- 
choanalytic help changed considerably. More and more frequently, 
these people displayed, not any of the circumscribed symptoms 
mentioned above, but what is often called a neurotic character. Such 
people find it difficult to work, to have satisfactory relationships with 
other human beings, especially in their marriage; they are overanx- 
ious, overambitious, or on the other hand suffer from lack of self 
confidence and from feelings of inferiority. It became increasingly 
clear to Freud that these characterological defects were also produced 
by forces unconscious to the person, and that character itself could 
be changed if the patient gained insight into the unconscious 
forces which had assumed control of his life. In fact, he came to see 
what while specific symptoms are the more dramatic and, in an ob- 



374 What Is Science? 

vious sense, the more painful expressions of unconscious conflicts, 
the neurotic character is what really matters; and these symptoms 
will be only superficially eliminated unless the whole character in 
which they are rooted is changed. 

So far we have spoken only of the form of mental disturbance com- 
monly called neurosis. A much more severe type of mental illness is 
known as psychosis. The neurotic person has retained a grasp of 
reality at least to the extent that he can function in society. He may 
bend reality, but he does not rend it. The psychotic person has so 
completely withdrawn from the outer world that the only reality he 
knows is that within himself. He hardly responds to events or people 
and thus Freud thought him incapable of the kind of relatedness to 
the analyst which was necessary for the analytic cure. However, a 
number of pioneering psychoanalysts have begun to break through 
this barrier. The psychoanalytic treatment of schizophrenia was first 
inaugurated by Harry Stack Sullivan at the Sheppard and Enoch 
Pratt Hospital, then by Bullard and Frieda Fromm-Reichmann at 
Chestnut Lodge, and by the Menningers at their clinic. In more re- 
cent years psychotherapy of psychoses has been taught and practiced 
at the Henry Phipps Clinic at Johns Hopkins, at the psychiatric de- 
partments of Yale and Harvard Universities, at the Austen Riggs 
Center and other medical schools and private hospitals, and by a 
number of individual analysts, both in the United States and abroad. 

The method of psychoanalytic cure is implied in what has been 
said about psychoanalytic theory. It is based upon the analysis of free 
associations, dreams, transference, and resistance. Its aim is to arrive 
at an insight into the desires and ideas which motivate the patient 
but of which he is not conscious. The essence of psychoanalytic ther- 
apy is to help the patient to recognize his own inner reality, to re- 
move the veils of rationalization, to gain strength by developing his 
reason and objectivity. The method which Freud discovered is indeed 
an application of the ancient precept "know thyself to the cure of 
mental illness. It must be emphasized particularly that psychoanalysis 
has nothing to do with persuasion and giving advice to the patient; 
it is the exact opposite of such methods. It rests upon the belief that 
the patient must make his decisions for himself, and that the func- 
tion of the analyst is only that of helping and stimulating him to 



Psychoanalysis 375 

gain increased insight into the forces which motivate his behavior. 

These general principles are common to all schools of psycho- 
analysis, but ideas about the particular contents of the unconscious 
depend on the various theoretical expectations held by the differ- 
ent psychoanalytic schools. 

As to some practical aspects of psychoanalytic treatment, it must 
be said that it is rather lengthy, lasting from one year, to two, three 
or four, or in exceptional cases even longer. In this respect it hardly 
differs from the length of treatment in any number of chronic ill- 
nesses. However, in recent years increasing efforts have been made 
to shorten the length of the treatment. Unfortunately, psychoanalysis 
is also expensive, as are all other treatments which require considera- 
ble medical assistance. The fees for analysis are normally somewhat 
lower than those a specialist in other fields would charge for an equiv- 
alent amount of time, yet they are high enough to make analytical 
treatment exceedingly difficult for people below the middle-class in- 
come level. Analysis has been extended as yet to only a small extent 
by various psychoanalytic institutes which have set up low-cost 
clinics. Of course, the demand always exceeds the time available for 
patients in these clinics. 

The therapeutic success of psychoanalysis cannot easily be reduced 
to statistics. Success depends partly on the severity of the mental dis- 
turbance, and very often people come to the analyst only after all 
other treatment has failed. It depends also on the skill and experience 
of the individual analyst. And, perhaps even more than other medical 
statistics, "cure/' "improvement/' and "negative outcome" are some- 
what subjective criteria. The most that can be said today is that psy- 
choanalysis is the only method of cure which promises any help 
in many cases of mental sickness. Secondly, that a large number of 
even severe cases of mental sickness are cured by analysis, while 
many others are not. Thirdly, that unless the analyst makes serious 
professional mistakes, treatment rarely harms the patient, even if it 
does not help. 

Analysts go through a rigid course of training, which lasts four 
years or more, and the center of which is their own analysis, and the 
supervision of their own analytic work by a teacher. By undergoing 
psychoanalysis, the analyst learns the method of free association 



376 What Is Science? 

and dream interpretation from the inside. Furthermore, he convinces 
himself of the presence of unconscious strivings by the discoveries 
he makes about himself in his own analysis. This also alerts him 
to his own blind spots and to irrational strivings which would di- 
minish his ability to help his patients. 

Originally, the psychoanalysts in each country were organized in 
societies which were part of an international organization under the 
leadership of Freud. These societies were responsible for the institutes 
which gave the above-mentioned training to candidates. In recent 
years, psychoanalytic associations and training institutes have been 
founded on premises which differ more or less from Freud's teachings. 
Also, some universities have instituted psychoanalytic training as part 
of the university curriculum (for instance, Columbia University, the 
National University of Mexico, and others). Freud himself thought 
that the practice of psychoanalysis should not be restricted to physi- 
cians, but should be exercised by students in other fields of the sci- 
ence of man. His view was accepted in all psychoanalytic institutes 
except those of the United States, but in the last few years a change 
has taken place in the United States too. Universities have trained 
psychologists in the handling of psychic difficulties, and some psycho- 
analytic institutes have admitted clinical psychologists to psychoana- 
lytic training. 



3. Further Developments in Psychoanalysis 

Freud laid new foundations for our knowledge of man; but although 
a genius, Freud was naturally a son of his time, and as with all other 
scientific discoveries it is to be expected that the generations standing 
on Freud's shoulders will modify his theory in many details. 

Even during Freud's lifetime some of his closest disciples suggested 
new theories which, like most later developments, had in common a 
questioning of Freud's assumption of the primary role of sexual striv- 
ings. Unfortunately, most of these theoretical deviations led to per- 
sonal antagonisms, and to the foundation of mutually hostile schools. 

The most important deviation from Freud's theory was developed 
by Carl }. Jung in Switzerland. Jung changed the concept of libido 



Psychoanalysis 377 

from that of sexual energy to general psychic energy; he saw in my- 
thology and religion expressions of profound human wisdom, rather 
than of infantile phantasies; he studied the connection between the 
great myths of various cultures, and the dreams and neurotic mani- 
festations of individuals, and made many brilliant contributions to 
the understanding of the unconscious as well as to that of religion 
and mythology. 

Alfred Adler, another of Freud's early disciples, also split from the 
original thought because he did not share Freud's belief in the su- 
premacy of the sexual instinct. But being less philosophical and more 
practical-minded than Jung, he put most of his attention on what 
might be called the tactics and strategy of life. He discovered the 
psychological significance of organic defects, and explained many 
character traits as compensations for such early organic inferiorities. 
He believed the main source of human striving to be the striving for 
power, by which he meant essentially social recognition and pres- 
tige. 

The last of Freud's disciples to leave his school was Otto Rank. 
Less systematic than Jung, yet like him interested in problems of cul- 
ture, art and philosophy, he developed a number of brilliant theories. 
At one time he thought he had found a basic cause for neurotic de- 
velopment in the anxiety occurring during birth (birth trauma). 
Later, he developed interesting ideas about the connection between 
artistic creation and neurotic-symptom formation. The neurotic per- 
son refuses the pretense of role playing, which in Rank's view is char- 
acteristic of the average man, but at the same time he is unable to be 
creative like the artist. 

Another, and one of the oldest and closest of the disciples of 
Freud, Sandor Ferenczi, never broke with him and the official school, 
although he developed toward the end of his life ideas which dif- 
fered from Freud's, and which were never accepted by the latter. In 
contrast to Freud's idea that the analyst should be an objective ob- 
server, quite detached from the patient emotionally, Ferenczi insisted 
that love is not only the necessary leaven in all living, but that it is 
especially necessary in the healing work of the therapist. 

In the last twenty years, certain changes have been taking place 
both within and without the Freudian school. Within, develop- 



378 What Is Science? 

ments are mainly centered upon greater study of the ego devel- 
opment (Hartman, Kris, Walder and others); the application of 
psychoanalysis to anthropology (Geza Rohheim and Abram Kar- 
diner); psychosomatic diseases, and brief psychotherapy (Franz Alex- 
ander and his associates), and the psychoanalytic study of psychoses 
already mentioned. A tendency which differs markedly from that of 
most Freudian psychoanalysts is to be found in the Southern German 
and Swiss school of psychoanalysis (Gustav Bally and others). Com- 
mon to the thinking of this group is an emphasis on the philosophical 
and anthropological problems of human existence, and on a convic- 
tion that the full analytic understanding of man must deal with 
these problems. In Japan a group of psychoanalysts (Dr. Kenji Oht- 
suki) which fundamentally accepts Freud's theory tries to adapt it 
by introducing specifically Asiatic philosophic concepts. 

Somewhat more deviant from Freud's theory are those often called 
neo-Freudian (Harry Stack Sullivan, Karen Horney and Erich 
Fromm). Although they have certain features in common (em- 
phasis on social and cultural factors and a critical attitude to the 
theory of the primacy of the sexual instinct) they nevertheless differ 
considerably among themselves. Horney's theories are more remote 
from Freud's than the two others; in some respects they constitute a 
fruitful and constructive continuation of Adler's thinking. 

Without ignoring the significance of childhood experience Horney 
judges it less important, both for understanding and for therapy, 
than the events of the present. She places much emphasis on the con- 
flict between various "neurotic trends/' and on the role of anxiety in 
keeping these trends going. In trying to adjust himself to his environ- 
ment, the child, and later the adult, can move towards people, against 
them, or away from them, and Horney gives a brilliant description of 
what happens when these three forms of approach to the world are 
intermingled, and if none of them is brought to its full fruition. To 
move "towards people/' in the sense of becoming unduly dependent 
on them, leads to helplessness, "against people" to hostility, "away 
from people" to isolation withdrawal. 

Sullivan, who started his research with a profound new insight into 
the nature of schizophrenia, proposed later that, not the fulfillment 
of sexual desires, but a need for security and the avoidance of intense 



Psychoanalysis 379 

anxiety and the feeling of aloneness, were the central cravings of 
man. He considered the need for security, for intimacy and the satis- 
faction of lustful striving (sexuality) the motivating powers in man's 
psychic structure. Thus Sullivan does not put emphasis on sexual 
libido alone, but on the total organism as a psychobiological unit, 
and on the various forms of relatedness to the outside world which 
this organism can choose. It is characteristic of his viewpoint that he 
defined psychiatry and psychoanalysis as the study of "interpersonal 
relations." Sullivan's work is characterized by extraordinary respect 
for the mentally sick person, especially those suffering from schizo- 
phrenia. To have transmitted this respect to his many students is not 
of the minor achievements of this brilliantly gifted man. Like Freud, 
he saw in the earlier years of the child the root of his later develop- 
ment. He made one of the most minute and imaginative studies of 
the experiences of early childhood, and particularly the relationships 
between the child and significant persons around him. It must be 
noted that Sullivan had a keen interest in the application of psycho- 
analytic knowledge to problems of anthropology, sociology and 
politics. Although he did not write any larger study on these sub- 
jects, his influence on students in the social sciences was fruitful 
and extensive. 

Fromm believes that while man's physiological needs become im- 
perative motivations of action if not satisfied, they are not the basic 
inner forces which determine man's actions, feelings and thoughts. 
Only by considering the specific conditions of human existence, 
and its inherent contradictions, can we understand the basic forces 
and passions in man. Man is a "freak of nature"; lacking the instinc- 
tive equipment which regulates the life of all animals, but gifted in- 
stead with reason, imagination, and self-awareness, life becomes for 
him a problem which must be solved. He has to relate himself to 
others, to find a new rootedness to replace those roots in nature which 
other animals have; he must acquire a sense of identity (self) and a 
system of orientation and an object of devotion. Mental health is 
identical with the development of a productive orientation, the abil- 
ity to grasp the world in the realm of feeling by love, in the realm of 
thought by critical and imaginative reason, and in the realm of 
action by creative "work and art. The norms taught by all great hu- 



380 What Is Science? 

manist, religious and philosophical teachers are at the same time the 
goals which man must strive to attain in order to be sane. Fromm has 
emphasized the role of the socioeconomic structure on the character 
development of the individual. According to him, each society creates 
& personality type which "strives to \^ant to do what it has to do, and 
thus to transform the general psychic energy into energy useful for 
the particular purposes of a given society/' But these social needs can 
be, and often are, in conflict with needs stemming from the nature 
of man, and its inherent need for love, human solidarity and the 
development of reason. Insofar as a given society does not satisfy 
these human needs, it will produce a "socially patterned defect" com- 
mon to all its members. 

Among the group of neo-Freudians, Fromm has put most empha- 
sis on the criticism of society and its effect of stultifying and paralyz- 
ing man, not because contemporary society forces him to repress his 
sexual desires, but because it inhibits his faculty for critical thought, 
and tends to transform him into an automaton, into a marketing 
personality who loses the capacity for genuine and profound feeling 
and thought, and whose sense of identity depends on conformity. 



SCIENCE AS FORESIGHT 



JACOB BRONOWSKI 



Jacob Bronowski 



Jacob Bronowski was born in 1908 in Poland, but lived in Germany 
as a child during the First World War. From there he went to 
England in 1920, where he has lived ever since. He was trained as a 
mathematician, being a wrangler in the University of Cambridge 
(the name given there to a student in the highest class of honors in 
mathematics) and gaining his M.A. and Ph.D. in 1933. In the fol- 
lowing years, he published numerous papers in algebraic geometry 
and topology, and more recently in mathematical statistics. From 
1934 to 1942 he was Senior Lecturer in Mathematics at University 
College, Hull. He left university teaching in 1942 for wartime re- 
search, became head of a number of statistical units dealing with the 
statistical and economic effects of bombing, and was a pioneer in the 
development of operational research methods. At the end of the war 
he was Scientific Deputy to the British Chiefs of Staff Mission to 
Japan in 1945 and wrote the classical British Report "The Effects of 
the Atomic Bombs at Hiroshima and Nagasaki" For a time he served 
at UNESCO as head of the Projects Division, and from 1947 to 1950 
engaged in applying statistical research to the economics of industry. 
He is now Director of the Central Research Establishment of the 
National Coal Board, from which post he was granted leave of ab- 
sence in 1953 to visit the United States as Carnegie Visiting Profes- 
sor at the Massachusetts Institute of Technology. 

His boyhood problem of learning English as a new language at the 

382 



about Jacob Bronowski 383 

age of twelve gave Bronowski an abiding interest in the literature of 
England and America. He has written two widely-known and much 
admired books on literature: The Poet's Defence (1939) and Wil- 
liam Blake: A Man Without a Mask (1944). He is well known for 
radio talks and dramas, including Journey to Japan and The Face 
of Violence; the latter won the Italia prize for the best dramatic 
work broadcast throughout Europe during 1950 and 1951 and has 
recently been published in book form with an introductory essay 
which analyzes the modern impulse, in life and in literature, toward 
violence and crime. Bronowski has done solid mathematical work; in 
recent years its emphasis has changed from pure mathematics to 
statistics as he has grown more interested in the nature of probability. 
A subject to which he has devoted a good deal of thought and on 
which he has written some first-rate papers is the nature of scientific 
thinking and what logical and mechanical systems and machines can 
do to help explain it. He has concerned himself with the logic of 
experiment and with a broad range of philosophical problems bear- 
ing on the anatomy of research and scientific method. 

The combination of scientific and literary interests has bade Bro- 
nowski a leader in the modern movement of Scientific Humanism in 
England. His book The Common Sense of Science reinterprets the 
development of scientific ideas in a way which makes them meaning- 
ful to scientists and nonscientists at the same time. It is a gracefully 
written, lucid and penetrating essay. He is now working on a sequel 
to it, based on a series of lectures he gave at the University of Oxford 
in 1951, which looks broadly at the place and responsibility of the 
thinker (scientific, literary and social) in the modern world, under 
the title The Draught of Hemlock. His courses on the Philosophy 
and History of Science in the School of Humanities at M.I.T. were 
concerned with the similar problem of making the concepts of sci- 
ence part of the developing culture of the modern world. His three 
public lectures on this theme are about to be published under the 
general title Science and Human Values. 

Bronowski is married and has four children. He lives with his family 
at Cheltenham. For hobbies he plays chess and squash rackets ("I 
like watching all professional sport'' he writes); he enjoys reading 
old and modern poetry, but no novels. "I detest detective stones and 



384 What Is Science? 

science fiction and all purely constructive or ingenious writing I 
want writing to have human character and a philosophy, two things 
which I find moving in the theater more often than elsewhere" Al- 
though he claims to be not very knowledgeable about music, his taste 
being confined to modern music, he is writing an opera (called My 
Brother Died) with a young English composer, Peter Racine Fricker. 
With all this, nine-tenths of his reading and thinking remains in 
science and the philosophy of science. The essay which follows is an 
exceptional achievement as to scope, clarity and readability. Bro- 
nowski manages in less than 1 5,000 words to impart to the reader a 
clear understanding of a sprawling but fascinating subject whose 
topics include computers and logical machines, the theory of games 
and information theory, cybernetics, the logic of experiment, the 
nature of human thinking and the light cast upon it by the study of 
automata. He has asked me to acknowledge the helpful advice he has 
had from Mr. D. G. A. Thomas, particularly in the preparation of the 
diagrams. 



SCIENCE AS FORESIGHT 

JACOB BRONOWSKI 



1. Introduction 

Man is plainly distinguished from other animals by his control of 
his environment. An animal can perhaps make a shelter, migrate, or 
learn to change some of its habits; beyond this, it can do little to 
counter the rigors of its world, and must fit into them much as it finds 
them. By contrast, man has remade his world. He takes his climate 
with him; he has invaded the sea and the air, has changed his speed 
and his skin and his senses to his own design, and lengthened his life 
several times over. We marvel at the stick insect and the crocodile bird 
because they are so ingeniously adapted to their environments. But 
the example of man shows that the most successful adaptation in evo- 
lution is intelligent flexibility. By this one gift, the human population 
has come to dominate the world, from a total of some tens of thou- 
sands in prehistory to two and a half billions today. 

Man has changed the world by acting as (what Benjamin Franklin 
called him) a tool-using and tool-making animal. The obvious tools 
for this purpose are those which shape things and those which move 
things. To rearrange or, better, to reorganize matter by these means 
is our main skill and work. Even the African negro uses the knife for 
one and the bow for the other; and so other races use the plough and 
the wheel, the lack of which has kept the African more primitive 
than the cultures of Europe and Asia. 

385 



38A What Is Science? 

But the tools which shape and those which move, the power tools, 
are not the only world-changers. The Egyptians, who had the plough, 
also studied the flooding of the Nile, and made themselves great by 
coupling the two skills. Knowledge can be a means to control nature 
as power can. The study of astronomy in navigation was as helpful as 
the wheel and the sail in building the trade of Europe in the Middle 
Ages. 

There is thus another set of human tools, the tools of information 
and control. In ancient astronomy, the cross-staff and the astrolabe 
were such tools. Today the telescope, the camera, the spectroscope, 
the photoelectric cell and the automatic scanner, and many others, 
are extensions of these. Every laboratory is cluttered with such in- 
struments, which enlarge our "intelligence" in both meanings the 
military meaning, and the everyday one. 

Machines, like animals, have in fact evolved in two directions: the 
one toward muscle or strength, and the other toward brain or fore- 
sight. It happens that in the last two hundred years, since the Indus- 
trial Revolution bred first water-driven and then steam-driven ma- 
chines in England, we have been preoccupied with the power-hungry 
machines. Technology during these years has been goaded by the 
search for power electricity, chemicals, and now nuclear fuels. As a 
result, the machine of intelligence has usually been thought a labora- 
tory instrument only. But this is to overlook some of our most impor- 
tant inventions. The basis of modern life is the clock; and it was for 
improvements in the clockwork (then for the purpose of finding one's 
longitude at sea) that the British government offered (and tried to 
avoid paying) perhaps the largest cash prize in the history of science, 
in the eighteenth century. Since then the automatic timer, the switch 
and the fuse, the telegraph, the Morse Code, the telephone, the type- 
writer, the tape recorder, have grown as necessary to modern industry 
as the dynamo and the internal-combustion engine. Edison founded 
his career on his patents in a typical instrument of intelligence, the 
stock ticker. 

In short, the machine of power and that of intelligence are com- 
plementary. Much of man's power derives from his discovery of fire; 
but as much derives from the discovery of speech and writing, which 
make it possible to hand on experience from generation to genera- 



Science as Foresight 387 

tion, almost as Lamarck once thought evolution might act. Early ma- 
chines were largely such devices of knowledge and control the clock, 
the quadrant, the printing press, Leonardo's wind vane and his ele- 
gant machine for controlling the cutting of teeth on a file. (Leonardo 
did not understand the demands for power which other machines 
make; this is why his flying machines were merely a dream.) Then for 
the two great industrial centuries from about 1750, the drive was for 
power (rather than control) to shape nature until the nucleus gave 
us all we are likely to need. And as physics has now given us power 
from the nucleus at the center of the atom, so it has given us a new 
source of control and intelligence on the outskirts of the atom, from 
the electron. It is characteristic that the two machines whose names 
became catchwords at the end of the war were "nuclear pile" and 
"electronic brain." 

I have been lumping together three kinds of power tools: gener- 
ators of power, such as the nuclear pile; converters of power, such as 
the electric motor; and users of power, such as the trip hammer. It 
is not relevant to this essay to distinguish among them, since they 
all contribute to the reshaping of the world by physical strength. It is, 
however, important that I distinguish between the different kinds of 
control mechanisms and processes which can be used, and which 
form the subject of this essay. 

We can use knowledge to help us control our relations to our en- 
vironment, because it gives us foresight. That is, experience encour- 
ages us to believe that the future follows the past in a repeatable 
pattern; and knowledge helps us to isolate and to forecast this pattern. 
The subject we are studying is therefore foresight. We take the first 
step to this by accumulating observations; but I shall not discuss in- 
struments of observation, because they provide only the raw material 
for foresight. For example, I am not interested in the automatic 
voting machine or the census taker, as such. 

But once these data, the votes and the census record, have been 
taken, they allow us to make predictions about future votes and cen- 
suses. Now the forecasting machine enters for the first time; and I 
shall begin with the giant calculators, to show how such a machine 
digests its information and then projects it forward into a new setting, 
an election or a census. 



388 What Is Science? 

Machines of this kind, I shall show, are distinguished by nothing 
but their speed. In type, they remain purely deductive machines, and 
even if their forecast is wrong time and time again, they have no ca- 
pacity for changing its basis. They cannot learn from their own mis- 
takes. 

It is therefore appropriate to go next to machines which do have a 
mechanism for adaptation and learning. These machines, which 
change not only their answers but their approach to a problem as 
a result of their own findings, form an interesting analogue to the 
human brain. 

Once we are talking about mechanisms for adapting behavior, we 
enter the field of the strategy of foresight. There is now no longer just 
one way to get to our goal, the control of a situation; we have to find 
how to shift our procedure with the results we achieve. We are here 
entering the theory of strategy and of automatic controls of the sub- 
tlest kind. 

The more we press into such problems, the more we find that un- 
derlying them is a deeper problem: to grasp the right arrangement of 
the facts on which we proceed. This is the theory of communication 
and information. And I apply it finally to the nature of human and 
scientific enquiry in general not only how we foresee the movement 
of the world, but more deeply how we understand it. 

In this way, we begin from the machines which are poor copies 
(and copiers) of the essential steps in human logic and foresight; and 
we use them step by step to teach us something of what the mind can 
do better, in deduction, in comparison, and finally in imagination, 
until we see of what the mind's meaning itself is made. Our procedure 
in this essay is to learn by constantly pushing forward, beyond the 
field which each machine or process can explore, in turn, into the 
more complex actions of which it falls short. 



2. Deductive Machines 

I have made the point that there are two kinds of human tools or ma- 
chines: those which are, as it were, extensions of the hand, and those 
which are extensions of the brain. (In man himself, these two func- 



Science as Foresight 389 

tions are related, and there is fossil evidence that the enlargement of 
the brain followed, in human evolution, the development of the 
hand.) 

This essay is concerned with extensions of the brain, and what they 
have to teach us about the brain. I therefore begin with the simplest 
of all aids to the brain, and what not long ago would have been 
thought the dullest: the calculating machine. 

i) Analogue Machines 

There are many devices which will serve to simplify special calcula- 
tions. The engineer's slide rule (which depends on Napier's invention 
of logarithms just after 1600) simplifies multiplication and division, 
and this and other slide rules can be made to solve other special 
problems. Or we can build machines which take advantage of some 
natural relation, say the law of electric conduction discovered by 
Georg Simon Ohm, 

current = potential difference/ resistance, 

in order to carry out multiplication and division. 

Devices of this kind of which Diagram 1 is a practical example 
use the analogy between our problem and some natural process and 
are therefore called analogue machines. They are compact and cheap 
to build for small problems, but they have two drawbacks. They are 
rather inflexible in use, so that they cannot easily be put to new 
problems; and in a sequence of steps they tend to accumulate their 
errors, so that their accuracy is limited. 

For these reasons, the analogue machines are neither as useful nor, 
inherently, as interesting as machines which keep close to the basic 
procedures of arithmetic. I shall confine myself now to the latter, 
which use the ordinary numbers or digits to work with, and are there- 
fore called digital machines or, as I prefer to call them, arithmetical 
machines. 

ii) The Arithmetical Machine 

The processes of arithmetic are all rooted in counting, and all arith- 
metical machines are really counters. The simplest digital machine is 
therefore the clock, which fundamentally counts notches or impulses 



390 



What Is Science? 




Mine layout 





DIAGRAM 1 



An Analogue Machine 

The pressure drop along a mine airway is proportional to the square 
of the airflow. The potential difference along an electric resistance, 
however, is directly proportional to the current flowing. Hence an 
ordinary electric network is not an analogue to a mine layout. 

But if each element in the network is a filament which is heated 
by the current flowing through it, its resistance will itself change in 
proportion to the current; and therefore the potential difference now 
becomes proportional to the square of the current. Hence problems 
on the ventilation of mines can be (and are) solved on an electric 
network of the kind shown here, in which the air resistances are simu- 
lated by heated filaments. The distribution of pressures in the airways 
is given by the potential differences in the network, and the airflows 
by the electric currents flowing. 




Electrical analocut 



Science as Foresight 391 

(assumed to be regular) and registers its count on dials. (By con- 
trast, the egg timer and the water clock are analogue machines.) Elab- 
orate clocks which go on to register the date, the day of the week 
and the phases of the moon show this principle of counting very 
clearly. 

This principle was first built into an adding machine by the French 
mathematical (and religious) prodigy, Blaise Pascal, in 1642, when 
he was 19. His machine adds (for it still exists and works) as machines 
have done ever since, by turning a toothed wheel so many notches; 
the wheels are geared so that ten notches on one wheel shift the next 
wheel forward a single notch. The cash register, the mileage counter 
on an automobile, the automatic record on a Geiger counter, and a 
thousand such devices, still use Pascal's mechanism. 

In 1673 another philosopher and mathematician, Gottfried Wil- 
helm Leibniz, fitted to Pascal's machine the device which multiplies 
a number by adding it over and over again. A machine which can 
add can, of course, also subtract, by going in reverse; and usually a 
machine which can multiply can also divide. (Diagram 6, however, 
shows that this is not always so simple as it sounds.) Thus the Pascal- 
Leibniz machine was able to carry out all the familiar steps in arith- 
metic. In essence, the calculating machine for nearly 300 years 
remained as these two great men made it, and as we see it (somewhat 
electrified) in banks and accounting houses. 

iii) The Problem of Speed 

The large electronic machines have now replaced the toothed wheel 
by a tube or a circuit. This has not changed the principle of the arith- 
metical machine; it has merely changed its speed. As Diagram 2 shows, 
a tube or a circuit is still a device for counting; it simply counts much 
faster than a notched wheel. The difference is one of scale, just as 
the difference between chemical and nuclear energy is one of scale. 

In the case of energy, the scale is set by comparative distances: the 
distances between the parts of the nucleus are about a million times 
smaller than the distance between atoms, and therefore the fission of 
the nucleus releases about a million times more energy than does a 
reaction which breaks chemical bonds between atoms. 

In the case of counters, the scale is set by comparative speeds. The 



392 



What Is Science? 




DIAGRAM 2 

The Circuit as a Counter 

The left-hand circuit A shown here counts or 1; when it reaches 
2, it carries it forward to the right-hand circuit B, which counts or 1 
pairs. When the right-hand circuit reaches 2 pairs (that is, 4), it 
carries it forward to the next circuit C on the right, which is not 
shown; and so on. 

As the diagram shows, each circuit contains a pair of tubes; at any 
moment, only one tube of the pair (0 or 1 ) is conducting. The current 
is transferred from one tube of a pair to the other when a pulse is 
received from the preceding circuit on the left. The table below gives 
the number of pulses which have been counted, and the tubes which 
are conducting, at each count. The correspondence between numbers 
and tubes is particularly simple when the numbers are written in the 
binary notation explained in Diagram 7, and a column has been added 
on the right to show this. 

Number in 

Binary 
Notation 


1 

10 
11 

100 



Number 
Counted 


1 
2 
3 
4 



Tubes Conducting 
B A (initial condition) 
O B !A 

IB A (pulse has been carried to circuit B) 
IB!A 
lc OB A (pulse has been carried to circuit C) 



Science as Foresight 393 

tube or the circuit uses electrons to transmit its impulses, and they 
move at a speed comparable with the speed of light. The notched 
wheel uses mechanical pressures, and they are transmitted at a speed 
comparable with the speed of sound. Since light travels about a mil- 
lion times faster than sound, the tube or the circuit counts about a 
million times faster than docs the notched wheel. 

When a machine works as fast as this, it sets a new problem: How 
are we to keep up with it? This is the problem which has transformed 
the new machines and given them their unexpected interest. 

An electronic machine can multiply two numbers, each the size of 
the National Budget, in less than a thousandth of a second, and adds 
them in a tenth of this time. Nothing has been gained by these fab- 
ulous speeds if the operator has now to spend minutes in comparing 
the answer with some other result, and in arranging the machine to go 
on with the next step. lie might as well have done the addition and 
multiplication too on an ordinary accounting machine; it would only 
have added a few seconds to his total time. 

The electronic machine is quick at arithmetic; and if we are to take 
advantage of this speed, we must make it as quick at the other logical 
processes which go into solving a complete problem. When the ma- 
chine has reached an answer at one stage, it must be able to link this 
to some other part of the calculation and to continue of itself. That 
is, it must be able to store and to follow a sequence of instructions 
which has been given in advance, some of which are conditional in- 
structions say, to choose the larger of two numbers which it has 
found, and to work on with this. It must be able to store, compare 
and use its own answers at each step. 

When a machine can work to a well-planned, orderly and repetitive 
program like this, its output is hair raising. A dozen machines are 
now chugging away, on both sides of the Atlantic, on calculations of 
atomic structure, of the nuclear processes by which matter was or is 
built up, of aeronautics and gunnery, and of large-scale statistics. The 
speed of the machine in digesting detailed statistics has now been 
shown in several elections, and the presidential election of 1952 will 
serve as an example. In that election, President Eisenhower won a 
spectacular and unforeseen number of electoral seats. Nevertheless 
when, forty minutes after the poll closed, UNIVAC made a forecast 



394 What Is Science? 

based on the first two million votes, it differed from the correct final 
distribution of electoral seats by less than one per cent. I ought to 
add that the experts in social assessment of course disbelieved the an- 
swer and hastily shushed the machine. The distrust of exact calcula- 
tion is deep-seated, and continues to keep it out of national statistics 
and economics. 

iv) A New Arithmetic 

The electronic machines are remarkable for their speed and there- 
fore for the amount of work they can do in a manageable time. They 
do this not by their complexity but by their simplicity. Like the hu- 
man brain, they achieve complexity only by the repetition of simple 
elements tubes or circuits, where the brain repeats the same unit 
cells. Their strength, in fact, is repetition; we tax their logical appara- 
tus least, and make the most of their arithmetical speed, by breaking 
down a problem into very simple steps, which are taken over and 
over again. Diagram 3 is a hypothetical but illuminating example of 
how a mathematical process (squaring a number) might be broken 
down for some machines (into primitive and repeated additions). Dia- 
gram 4 shows the instructions which the machine would receive for 
this purpose. 

No mathematician will square a number as Diagram 3 docs be- 
cause the labor of simple repetition will take him many hours, and 
expose him to the constant danger of making mistakes, from tedium 
or inattention if for no other reason. But the machine is inured to 
tedium and inattention, and fairly safe from error; and simplicity and 
repetition are what it is best at. 

Thus the large machines run counter, in many ways, to the trend 
of mathematics. Mathematicians have always looked for short cuts, 
devices to avoid tedious work, and contractions of processes. In a 
sense, all mathematics is the discovery of short cuts (algebraic geom- 
etry, the integral calculus, and complex functions are examples), 
and the avoidance of repetitive methods such as trial-ancl-crror and 
step-by-step approximation. But the machine asks us to go back on all 
this and to seek instead for precisely the opposite: for ways to break 
the problem into small, repetitive parts, over and over again, and step 
by step. (For this reason, the machines have been used from the out- 



Science as Foresight 395 

DIAGRAM 3 

Machine Procedures are Simple and Repetitive 

A mathematician asked to square the number 8,921 does it by 
multiplication: 

8,921 
8,921 



71,368,000 

8,028,900 

178,420 

8,921 

79,584,241 

A machine might find it more convenient on occasion, (say, when 
compiling a table of squares for permanent record) to use the simple 
repetitive device of adding the odd numbers, as follows: 

1= 1=1X1, 

1+ 3 = 4= 2X 2, 

1+ 3 + 5= 9= 3X 3, 

1+ 3+ 5+ 7= 16= 4x 4, 

1 + 3 + 5 + 7 _|_ 9 + 11 + 13 + 1 5 + 17 + 19 = 100 = 10 X 10, 



and so on until the machine reaches 
1+3+5+7+ .................................................. 

................................... + 17,841 = 79,584,241 = 8,921 x 8,921. 



396 What Is Science? 

DIAGRAM 4 



Programming a Machine to Carry out a Simple Repetitive Procedure 

Below are given the formal instructions to a machine to carry out 
the procedure for squaring a number by the method of Diagram 3. 
These instructions will be understood more easily if the procedure is 
first sketched in general terms. It consists of three kinds of steps: 

(i) The odd numbers are built up one after another (in Store 2), 
beginning with the number 1, by adding the number 2 over 
and over again. 

(ii) A count is kept (in Store 3) of how often this remains to be 
done, in order not to overshoot. 



Meanwhile, the steps shown in Diagram 3 are carried on, namely, 

(iii) The odd numbers obtained (in Store 2) are added up, as they 
are obtained, in Store 5, where the answer will be reached 
after the right number of steps (controlled by (ii) above). 



Once the general method is understood, it is clear that the machine 
need be able to do only three things: 

A. Read the number in one Store and add it to another Store; 

B. Read the number in one Store and subtract it from another 
Store; and 

C. Inspect one Store and stop the calculation when zero is reached 
there. 



For the control of the machine, orders are read in sequence from a 
tape, and it greatly increases the capabilities of the machine if several 
Tape Readers can be used at will. It is therefore convenient to have 
a further order, 

D. Change from one Tape Reader to another. 



Science as Foresight 397 



DIAGRAM 4 continued 




Input 
(orders) 



Here is a functional diagram of such a machine. 
The orders for this machine are given in three parts: 



Part 1 

A. Add 

B. Subtract 

C. Inspect 

D. Change source 
of order. 



Part 2 

Store from which 
number is to be ob- 
tained. 

Store which is to be 
inspected. 

Input tape which is 
to be used. 



Part 3 

Store into which num- 
ber is to be added (or 
subtracted). 

Not needed (Zero). 
Not needed (Zero). 



Three tapes arc used: Tape I for the numerical data, and Tapes II 
and III for orders. The orders have been split between Tapes II and 
III because it is convenient to put orders which are repeated many 
times during the calculation (subroutines) on a separate tape. The 
subroutine Tape III is often a closed loop, as here. 

Only three numbers are needed on the data Tape I: they are 2, 1 
and 8,921 (the last is the number to be squared). The groups of num- 
bers required on the other tapes are shown below. The program 
has been designed so that Tape II is used only once; Tape III is used 
8,921 times. The machine starts by reading Tape II. 



398 



What Is Science? 



DIAGRAM 4 confinoed . 

TAPE II 

Order What Happens 

A. 6. 1 First number (2) on Tape I added into Store 1. 

A. 6. 2 Second number ( 1 ) on Tape I added into Store 2. 

A. 6. 3 Third number (8,921) on Tape I added into Store 3. 

A. 2. 4 Contents of Store 2 added into Store 4. 

D. III. Source of next and subsequent orders transferred to 
Tape Reader III. When Tape Reader III is op 
erating, Tape II is stationary, and hence when con- 
trol returns to Tape Reader II, the next order is read. 

A. 5. 7 Result in Store 5 printed. 

TAPE III. (which comes into operation after the fifth order on 
Tape II.) 

Order What Happens 

A. 2. 5 Contents of Store 2 added to Store 5. 

A. 1.2 Contents of Store 1 added to Store 2. 

B. 4. 3 Contents of Store 4 subtracted from Store 3. 

C. 3. Contents of Store 3 inspected. If zero, the next ordei 

is carried out; if not, the next order is omitted and 
the next but one carried out. 

D. II. Source of next and subsequent orders transferred to 

Tape II (which resumes operation with the sixth 
order). 

A. 2. 5 (This is a return to the first order on Tape III, which 
is a closed loop.) 

This is a hypothetical program, designed only to show the gen- 
eral principles on which a complicated operation is broken up into 
many simple steps for a machine. Few machines, in fact, would need 
to go to so much trouble in order to square a single number (because 
most machines, unlike that assumed in this example, are able to multi- 
ply directly). But notice that the program given here does have 
one advantage: it finds the squares of all numbers smaller than 8,921 
on the way to finding the square of 8,921. This program could 
therefore be used to record for future use a table of the squares of 



Science as Foresight 399 
DIAGRAM 4 continued 

all these numbers. (To do this, it is only necessary to add a single 
order to Tape III: the order A. 5. 7 after the fifth order on that tape.) 
The preparation of permanent tables of this kind is a useful applica- 
tion of large machines. 



set for calculations which naturally go from one result to the next, 
like those which make gunnery and other tables, or those which ex- 
plore point after point in a field of flow as in aeronautics.) And as 
Diagram 6 shows, stepwise approximation and trial-and-error are daily 
and powerful tools in the arithmetic of the machines. Most deeply, 
the machine demands that its work be reduced to the simplest, basic 
processes; and to plan a program for these machines is to work in a 
new and, as it were, perverse arithmetic. 

v) A New Political Arithmetick 

The great but essentially simple power of the machine in calculation 
brings with it also a new way of looking at its (and our) problems. 
Many problems in economics, social science and national planning 
are at bottom problems of statistical accounting. (For this rea- 
son these subjects were called by their inventors in the seventeenth 
century, political arithmetick, a graphic name which I am glad to see 
revived.) But the actual labor of accounting, the arithmetic of ex- 
amining all possible relations and interactions between the entries, 
has hitherto been unmanageable. Therefore these social subjects 
have, like the physical sciences, looked for short cuts in general prin- 
ciples. They have not been successful, largely I think because the 
subjects have lacked the experimental data from which laws in the 
physical sciences are crystallized. There are of course social and eco- 
nomic data in plenty, but they are unwieldy and uncontrolled, and 
no one has been able to isolate more than the barest trends from 
them. (When they have tried to do more in extracting some mathe- 
matical model from the chaos of markets and policies, as Professor 
Colin Clark has bravely tried, they have been as wide of the mark 
as was his forecast of an economic blizzard in 1954 based on the ex- 
perience of 1949.) 

The new machines offer us the chance of handling massive social 



400 What Is Science? 

and economic data without any preconceptions at all. In this way, 
even the limited variations in national statistics can become the basis 
of an experimental approach, but one different from the physical 
sciences. In the physical sciences, the variables are in the main under 
our control, and it has therefore been possible to evolve an experi- 
mental technique of simplification, for example by varying one con- 
dition at a time. Social and economic results cannot be handled in 
this way; they must be explored for their hidden interactions and 
correlations as they stand, without the assumption (which physics has 
held for 600 years since William of Ockham) that laws shall be 
simple. By making this possible, the fast machines open the prospect 
of a new intellectual approach to the aims of statistics, and beyond 
that a new empirical approach to national planning. Where calcula- 
tion in the past has been so crude, there has been an excuse for the 
planner's preference for his own (optimistic) hunches, and his appeal 
to imponderables; he could hardly be more wildly out than Professor 
Colin Clark or the professional weather forecasters. But the adminis- 
trator's "imponderables" means at bottom the integrated impres- 
sion made in his mind by the complex of individually small shifts and 
nuances in the data, which have not been separately analyzed. Today 
there is no reason why they should not be analyzed and given their 
proper, ponderable weight. Thus the new machines may found a new 
social and economic science, which need no longer shirk the arithme- 
tic in political arithmetick. Its relation to current economic rules of 
thumb may be, roughly, that of UNIVAC to a traditional tag such 
as "As Maine goes. . . ." Indeed, the work of correlation which un- 
derlies the election forecasts of UNIVAC is a first example of the 
new methods. 

vi) The Logic of the Machines 

Let us turn back to take a last look at the workings of the new 
machines. I have remarked that these are forced on us by the speed 
of the machines; to take advantage of its speed, a fast machine must 
store, use and compare its instructions and its own answers. (This 
was foreseen in the design of a fast mechanical machine about 1835 
by Charles Babbage, who detested piecemeal calculation and organ- 
grinders.) How in fact is this done? 



Science as Foresight 401 

The instructions must be both permanent and rapidly scrutinized; 
they are therefore usually punched as holes in a paper tape essen- 
tially the device for storing information which Dr. H. Hollerith in- 
vented in 1891 when the U.S. census became unwieldy. Diagram 
5 shows a machine tape of instructions (for taking square roots). 
It makes for speed if all that the machine need note and obey as it 
senses the tape is "hole" or "no hole/' that is, a simple choice of 
"on" or "off," "yes" or "no." For this reason, most machines code 
both their orders and their arithmetic in a system which has only two 
symbols, "yes" and "no" which are usually written simply as "1" 
and "0." Diagram 7 shows how this arithmetic works. 

This system makes numbers a great deal longer than in everyday 
writing (over three times as long) and involves the "translation" of 
ordinary numbers into and out of it. Nevertheless, as Diagram 2 il- 
lustrates, the simplicity of so instructing and running a machine, and 
of making tubes and circuits for it, is usually held to outweigh this 
disadvantage. 

The instruction tape works the machine much as would the fingers 
of an operator pressing the keys of an ordinary accounting machine. 
But instead of registering each answer on a display panel, the elec- 
tronic machine holds it on a magnetized drum or tape, or some other 
dynamic record that is, a record which recalls its contents at regu- 
lar intervals. Meanwhile, the instructions send the machine on its 
next step, while the last answer remains stored on the revolving drum 
or record. When this answer is wanted, in order to compare or com- 
bine it with that found at another step, the machine follows instruc- 
tions which tell it to pick it up from the magnetic drum again. The 
operations of the machine are accordingly geared to the speed of the 
drum or other dynamic "memory." 

In this way, successive steps in a long calculation follow one an- 
other without outside interference, until the machine finally reaches 
a result which is to be permanently recorded. This it usually puts on 
a magnetic tape, and thence types. 

There is nothing recondite in these machines. Their steps are logi- 
cal, and they are possible because deductive logic can be formalized 
and therefore mechanized. Yet, direct and understandable as their 
mechanics are, they open an arresting query. The machine stores. 



402 What Is Science? 



DIAGRAM 5 

Program Tape 

This example shows how the instructions to a machine are set out 
as punched holes in a tape. (This particular tape carries the instruc- 
tions for taking a square root the reverse process to that illustrated 
in Diagrams 3 and 4.) 



DIAGRAM 6 



Step-by-Step Approximation 

Repeated approximation is a powerful tool in a calculating machine. 
For example, some machines have no separate mechanism for long 
division. Instead they use the fact that 

If 



y 2 , 



y n +i, 



is a sequence of numbers such that 



y n ), 



then the numbers y of the sequence rapidly approximate to I/a 
(provided the first number y is chosen reasonably). 

As an example, let us find by this procedure . , ^ a famous approxi- 
mation to TT known to the Chinese in the fifth century and rediscov- 
ered in Europe in the sixteenth century. We begin by finding 



Science as Foresight 403 

DIAGRAM 6 continued 

-, taking as first number in the sequence y ~ 0.01. We find 

y* <*y 2-ay n y n+1 =y n (2-ay n ) 

y = 0.01 1.13 0.87 0.0087 

y 1 = 0.0087 0.9831 1.0169 0.00884703 

y 2 = 0.00884703 0.99971439 1.00028561 0.008849556800 
y 3 = 0.008849556800 

Seven-figure accuracy has been obtained after only three repetitions, 
and gives (on multiplying by 355) TT = 3.1415927. A fourth repetition 
would give eleven-figure accuracy, which however is out of place here, 

since - is no longer a good approximation to IT beyond the sixth 
decimal place. 



DIAGRAM 7 

Binary Notation 

The notation is most simply explained by examples. Thus, the 
number 5 is rearranged, in binary notation, as 4 + 1> that is 

(1X4) + (OX2)+1 
and is written as 

101. 
The number 8 is rearranged as 

(1X8) + (OX4) + (OX2)+0 
and written as 

1000. 

The number which we write every day as 19 is rearranged as 16 + 
2 + 1, that is 

(1 x 16) + (0 X 8) + (0 X 4) + (1 X 2) + 1 
and written as 

10011. 



404 What Is Science? 

DIAGRAM 7 confinued 



We are accustomed to build up a number from units, tens, hun- 
dreds, thousands and so on; instead, the binary notation builds it up 
from units, pairs, fours, eights, sixteens and so on. 

One reason why the binary notation is convenient for machines 
is that it has very simple addition and multiplication tables: namely 

+ :=0, 1+0 = 1, 1 + 1 = 10, 

0X0 = 0, 1X0 = 0, 1X1 = 1, 

and nothing more. 



uses and compares its instructions and its own answers. These are the 
parallels to what in a human mind would be called a program of 
work, a memory, and the exercise of choice. They have made it tempt- 
ing to call these machines "electronic brains." But does it make sense 
to call what the machines do "thinking"? 

Plainly the machines are not original thinkers. They follow instruc- 
tions, and they break down if they meet a choice which has not been 
foreseen. But these are not in themselves inhuman attributes: to fol- 
low instructions and to break down in face of the unforeseen are 
both sadly human. The machine carries through a sequence of logical 
steps; it is today becoming more and more a logical machine rather 
than a mere calculating machine. If by thought we mean logical rea- 
soning, then the machine can think as well as we can. We are preju- 
diced against it only because, like other prodigies, it was taught by 
its maker instead of by a schoolmaster. 

That is: the essence of deductive logic is that it can be formalized; 
it can therefore be incorporated in a machine; and the machine can 
then deduce or reason from given data as well as we can. In this 
branch of reasoning, the machine is potentially our equal. If we 
want to claim more for our brains, we must turn to a larger field 
than deductive reasoning. 



Science as Foresight 405 

3. Adaptive Machines 

The obvious shortcoming of the purely deductive machine is that it 
cannot learn. It cannot gain from its experience, because it cannot 
change its own method. Its procedure is inflexible, and the machine 
cannot itself adapt it to changes. 

In this sense, the deductive machine, although it may control a 
whole assembly line or an automatic factory, imitates only the in- 
stinctive behavior of animals the wonderfully complex but (in the 
main) fixed sequence of actions of a gall wasp or a burying beetle. 
Before, therefore, we can begin to look in the machine for a model 
of intelligent procedure, it must include at the least some sign that 
it can modify its own course in order to reach its goal in changing 
circumstances. 

i) Goal-Seeking Strategy 

I have used the word "goal," which brings into the discussion the 
breath of an oddly sporting air. This is not, as might be thought, 
inappropriate. It is in fact not an accident that creatures of rigidly 
fixed behavior, such as the ants (some of which finished their evolu- 
tion fifty million years ago, and have not changed either their 
anatomy or their organization since) do not play games. There are 
students of animal behavior who regard play, in the fox cub, the 
young bear, or man, as essentially a training in choice, and the natu- 
ral mark of a growing freedom of behavior. 

Games of sport as we play them differ from our real life in this: 
that the purpose or goal of the contestants is simple and precisely 
defined, and the ways in which they may gain their goal equally are 
simple and limited. This is true, whether the game is an exercise of 
muscle or, in human beings, of mind, all the way from rowing and 
football to billiards and chess and to war. They are goal-seeking ac- 
tivities with rules. 

For this reason, games are natural models for all purposeful activi- 
ties, in which we can study with great clarity the strategy for reaching 
our aims in the competition of life. I shall therefore often illustrate 
the working of machines and of planning with precise examples from 



406 What Is Science? 

games, rather than vague generalizations from economics and the 
stock market. I am in this essay looking at all thinking as foresight, 
that is as the search for strategies which anticipate future events or 
moves; and as our language shows, in words like "goal," "competi- 
tion," and "moves," games are compact fields (itself a game-word) 
for this. 

ii) Unlimited Foresight 

I said that the deductive machines which I discussed in the last 
chapter cannot modify their own strategy, and must therefore proceed 
as it were only by instinct. This may seem unfair to any machine 
which has provision in it for choosing between two courses of action, 
by some criterion of purpose. Let me illustrate it by examples; first, an 
extreme and impractical example. 

Think of a machine into which we have wired the rules of chess. 
We could set it to work on a given position, and let it grind out in 
turn every possible consequence of every move, reaching always 
either mate, stalemate or the endless repetition of the same moves. 
In this way, we could (in theory) ensure that the machine made no 
move -which was not sure to win (if the initial position could be 
won). I have said "in theory" and that this is an impractical example, 
and so it is, in a position of any prolonged complexity certainly in 
the opening position of a game of chess. But I ought to add that an 
electronic machine has been programed to do just this for two moves, 
in order to solve two-move chess problems, as it were by brute force. 

In the game of draughts or checkers, the accumulated practice of 
players, as recorded in books, has over the years acted like such a 
machine, and has produced so complete a knowledge of the game 
that virtually nothing remains to be found. There is really no rea- 
son for playing checkers except human fallibility. Collective experi- 
ence has been a checkers machine which has analyzed every move to 
the end. We could therefore put this into a simpler machine: a 
mechanical reference book which consults itself after each move by its 
opponent, and in reply plays (without analysis) the move which 
book-analysis has shown to be best. A noughts-and-crosses ma- 
chine has in fact been built which plays just like this, automatically. 
This "fossilization of experience" can take another form. There is 



Science as Foresight 407 

a charming game which has the merit that it needs no apparatus ex- 
cept a box of matches, and is yet an intellectual tussle between two 
players if they do not know its theory. Diagram 8 gives the rules of 
this game of Nim and a characteristic position. 

As in the game of chess, we could wire a machine to grind out 
every possible consequence of every move in Nim. If this machine 
were faced with the position in Diagram 8, I have no doubt that, 
after a deliberation running to hours or days, it would make the 
winning move (there is only one). 

A knowledgeable human player will make the same move in a 
matter of minutes; and will make it, not by analyzing all the conse- 
quences of this position, but because he has already analyzed all the 
consequences of all positions. That is, he knows the theory of the 
game; for as Diagram 8 shows, the only demerit of this attractive 
game is that its theory is fully known. 

Here, then, the simpler course would be to build the theory into 
the machine, rather than the laborious capacity to analyze. (The way 
the theory rests on sub-piles of 16, 8, 4, 2 and 1 matches makes it 
particularly convenient to put into an electronic machine.) In fact, 
at the Festival of Britain in 1951, a machine was built in this way, to 
play Nim automatically; and Professor Norbert Wiener and I played 
a memorable session on it, against one another and against the ma- 
chine. In an intellectual sense, no doubt we knew the theory better 
than the machine; but the machine won, because its wiring (its 
"instincts") never made a mistake in applying the theory. 

In summary: a machine can be conceived to have unlimited fore- 
sight and to grind out a game to the bitter end. Such a machine, 
however, is impracticable unless the game offers few alternatives. And 
in such cases, it is easier to make the machine into a form either of 
memory or of instinct, which plays the right move because the right 
move is known from practice or theory, and has been built into the 
machine with no nonsense. 

iii) Experience in Machines 

I have shown that a machine can be arranged to prefer one move 
to another, and to respond to the moves which its opponent in a 
game of strategy makes, and still it is doing no more than follow a 



408 What Is Science? 

DIAGRAM 8 



The Game of Nim 

The contents of a box of matches are stacked in several piles, at 
random. The game is between two players who move in turn. A move 
consists in picking up a number of matches from one pile; the player 
can pick them from whichever pile he chooses, and he can take as 
many matches as he likes (including the entire pile); but he must take 
all his matches on one move from one pile only and he must take at 
least one match. The player who clears the table (that is, who picks 
up the last match or pile of matches) wins. 

Consider a characteristic position say when there are three piles 
left on the table consisting of 5, 8 and 19 matches. What should the 
player do who has the move? 

He should think of each pile as made of sub-piles of 16, 8, 4, 2, and 
1 matches, precisely as in the binary system explained in Diagram 7. 
Thus he thinks of the three piles on the table as 

(1X4) + (OX2)+1= 101, 

(1 X 8) + (OX4) + (OX2)+0 = 1000, 

(1 X 16) + (0 X 8) + (0 x 4) + (1 X 2) + 1 = 1 1 1. 

He should now pick up enough matches from one pile to leave an 
even number of each kind of sub-pile on the table. This is done by 
arranging that there is left an even number of 1's in each column on 
the right, above. Therefore, in this case, he must reduce the third 
pile to 



which means leaving thirteen matches in the third pile. The player 
who is to move therefore takes six matches from the third pile. In 
this way, he obtains a stranglehold which his opponent cannot break, 
and which he renews each time it is his turn to move again. 



Science as Foresight 409 

rigid routine. It is still working entirely by calculation, and when it 
does this the machine might as well follow either the ''reference 
book" or the theory of right moves which its designer could work out 
and build into it. In other words, the logical machine was "born" 
with all its procedures already ready-made; and while we admire such 
infant prodigies (who, characteristically, among human beings are 
usually remarkable only at chess, mathematics, music or languages) 
we do not rank them with those whose achievement is a response 
to their individual experience of life: with William Shakespeare, 
Thomas Jefferson or Johann Wolfgang Goethe. 

Nor are we satisfied with ready-made responses to stimuli. Many 
machines exist which adjust themselves to outside stimuli: the ther- 
mostat does so in a small way (as Diagram 9 shows), and the auto- 
matic pilot in a large. These machines "sense" the outside tempera- 
ture or wind, feed this information back into their mechanism, and 
automatically move to counter the outside change to raise the tem- 
perature, or keep the aircraft on an even keel. But there is nothing in 
this feeding back and subsequent response which distinguishes these 
from the machines which make a move in response to a move of 
mine. The thermostat and the automatic pilot feed back information 
on their environment and respond to it, continuously instead of from 
time to time: that is their only difference. They still carry out no 
more than reflex actions. 

We are looking for a machine (by which, of course, we mean es- 
sentially a process) which is genuinely modified by its experience: 
which accumulates experience, and uses it to change its procedure 
permanently, as a growing child docs. We are looking for a machine 
that learns, in the sense of changing its own strategy. 

There are several ways in which animals learn; of these, the most 
convenient to put into a machine is trial-and-error. Suppose, for ex- 
ample, we go back to our ideal chess-playing machine. We cannot 
really make this machine blindly follow to the end every conceivable 
sequence of moves. But we can make it pick out some moves to try 
and follow their possible consequences for five or six moves. Suppose 
that we let the machine play in this tentative way, with limited fore- 
sight, and give it a mechanism for deciding on a reasonable move 
on these restricted findings. Against a human player, this machine 



410 



What Is Science? 







Meter 








/^*^\ 






Thermometer ^""" 


* f M 


Arrows show 
direction of control 






Low 1 | I High 














Heating 5~ 

element < 


Controller 


1 Power 
/ supply 



















DIAGRAM 9 

Feedback 

In this thermostat, the thermometer measures the temperature 
which is to be controlled, and feeds back its finding to the meter and 
controller. If the meter shows the temperature to be below that which 
has been set, the controller steps up the power sent to the heating 
element and so raises the temperature. If the meter shows the tem- 
perature to be too high, the controller cuts down the power sent to 
the heating element and so lowers the temperature. 

The system is self-correcting, but fails if there is excessive or grave 
dislocation. For example, if the wires between the meter and the 
controller are accidentally crossed over, the system runs away. 



DIAGRAM 1 



An Ultrastable System 

The system is the same as that shown in Diagram 9, with one addi- 
tion: a relay has been added which (by means of a switch) reverses 
the connection between the meter and the controller if the meter 
reading remains persistently too high or too low. This system will 
therefore correct itself even if the wires between the meter and the 
controller have been crossed over. 



Science as Foresight 411 



DIAGRAM 10 continued 



Thermometer ^ -~ 



Heating 
element 




Power 
supply 



The relay could be designed to do more than simply trip the switch. 
For example, it could be made to explore different time lags and 
different control ratios between the meter and the controller. In an 
ordinary thermostat (as shown in Diagram 9), if the controller follows 
the meter too closely, the temperature constantly oscillates between 
too high and too low, and the system is no longer stable. Here, how- 
ever, the relay would correct this: it makes the system ultrastable. 

will often lose. But suppose we now put into the machine also a 
memory which counts its wins and losses, relates them to the moves 
chosen, and then steers the machine away from moves which lose 
repeatedly. By these means, the machine would learn in time (a long 
time) to keep away from losing lines and to choose winning lines. It 
would learn habits, not mere responses. 

They would not be habits of perfection; as in the human player, 
they would be the empirical result of playing with people. Indeed, if 
the machine played constantly against bad players, it would learn 
some very poor habits just as playing chess or tennis against inferior 
players teaches a human player bad habits, which are punished when 
he meets a good player. 

In this way, we can visualize a machine which truly learns from 
experience. In its simplest form, of course, the learning procedure by 
trial-and-error is no more than the acquisition of a conditioned reflex. 
The machine learns to "associate" a stimulus, namely an oppo- 
nent's move, with a result, namely win or loss. But our chess-learning 
machine adds to this an active element of exploration. For without 



412 What Is Science? 

deliberate exploration, what we or the machine get from the out- 
side world remains passive, and something less than genuine experi- 
ence. 

iv) The Exploring Machine 

The leading place which must be given to exploration has been 
recognized by those who look in the machine for a likeness, not to 
abstract thought, but to the behavior of the nervous system. A 
neurologist, Dr. Ross Ashby, has built a machine on these lines (and, 
in another direction, an expert in servomechanisms, Dr. A. M. Uttley, 
has studied the theory of similar processes). In this machine, ex- 
ploration is the task not of one fixed process, but of many small ele- 
ments of enquiry and decision. The machine has a large number of 
connections and internal paths, each with a simple "off or on," "yes 
or no" response. The task for the machine is to adapt itself to an 
"environment," that is to settle down under assigned conditions in 
a way which is stable. By this we mean, in the first place, that the 
machine shall change its state slightly when the environment changes 
slightly, and return when the environment returns. 

The thermostat and the automatic pilot are stable in this sense, as 
Diagram 9 shows; and so far, Dr. Ashby's machine may seem to do 
no more than they do, except that it finds its own stable states. When 
the conditions for the machine are set, it runs through many possible 
adjustments and connections quickly, in a random sequence, its ele- 
ments blinking "off or on" decisively at each attempt until it reaches 
a stable state. Its random connections have joined up to find and hold 
a path which remains stable under small changes in the environment. 

But the machine does not stop there. It also explores large 
changes in its (external or internal) environment, under which its 
first state may no longer be stable; and it will then run through its 
connections to find a new stable state. Thus the machine has the 
ability to reach and hold states which are stable in a much wider 
sense. The thermostat and the automatic pilot cannot follow excessive 
and gross changes; but Dr. Ashby's machine is ultrastable and can 
find a new stable state even after wrong wiring or injury. Diagram 
10 shows, in its simplest form, the principle which makes this possible. 
In the actual machine it is achieved, as it may be in the nervous sys- 



Science as Foresight 413 

tern, by having many small units or paths (cells in the brain, nerves 
in the body) whose connections are not rigid, but are run through 
on a system of probabilities, and so maintain a constant internal ex- 
ploration. 

v) Adaptation and Logic 

Let me summarize the ideas of this chapter. Its central question is, 
What is there in good thinking which is not logical deduction? A 
logical machine, such as UNIVAC, cannot improvise; it cannot, of 
itself, learn to change. That is, it cannot look ahead and adapt its 
processes to its goal. These are the deeper components of the ex- 
ploring mind. Can a machine be made to show such adaptation? 

In order that a machine may adapt itself to a changing environment 
or task, it must do two things. It must explore the different actions 
open to it. And it must feed back into itself the results of its efforts, 
so that it may choose the most successful. The second of these skills 
is not peculiar to adaptive machines; in essence, it exists in a logical 
machine, if the latter can follow alternative strategies. Many simple 
machines keep themselves adjusted to change by such feeding back: 
I have quoted the thermostat and the automatic pilot. In short, those 
are only reflex actions; they bear no semblance to thinking. 

If the machine is to do more than, as it were, jump when it is 
pinched, it must give the largest place to exploration. It must have 
many choices built into it at each of its steps. It need not be made to 
test them all, or to follow to the end the consequences of those it 
tries: neither a man nor a machine would ever make a move at chess 
if this were demanded. On the contrary, there must be built into the 
machine a mechanism which makes it take chances. For, above all, 
the machine must not haver. It should be built up of units which take 
decisive steps, off or on, yes or no, with no crisis of indecision. 

It has been shown that such machines can be designed to adapt 
themselves to change, and their behavior will remain internally sta- 
ble. More, they can do what no machine has done before: they can 
adapt themselves to injury. I have seen Dr. Ross Ashby remove the 
wiring from his odd machine, leave out some and connect the rest 
at random. The machine balked, but it worked; after a few minutes, 
the machine pointer was again following the environment pointer. 



414 What Is Science? 

Such machines imitate animal behavior: instinct, reflex and adap- 
tation. They remind us that we once learned some anatomy from the 
pulley and the lever, and that we now have something to learn 
about nerves and brain from the electric switch. 

It may seem perverse to ask of machines, What is thought? The 
question seems to turn nature upside down, as Jonathan Swift tried 
to turn it upside down in that terrible close to Gullivers Travels 
in which only the animals are noble and logical, and the men are 
brutalized by desire and irrationality. Yet Swift was trying to analyze 
the complex countercurrents of the human character; and our ques- 
tion also is an attempt to see two facets of the mind. Pascal, who in- 
vented the first calculating machine, called man "a reed, but a think- 
ing reed"; and put into that phrase Swift's contradiction, that man 
is ennobled above his weakness only by his mind. But as Pascal also 
remarked, the mind is not a calculating machine. We do not think 
only in logic; and man does not become irrational when his thought 
moves outside deductive logic. 

There is an activity of thought in the mind, an imaginative ac- 
tivity, which explores and puts together unforeseen likenesses. So far 
as we can now see, it is not imitated either by the logical machine or 
by the adaptive machine. But their conjunction has taken us two 
steps toward it; and we must now prepare to take the third step. 



4. Strategy and Its Safeguards 

I began with situations (in a game, or an economic or strategic 
problem) in which the choice before us was clear cut. There were 
several alternatives, the consequence of each of which was (in theory) 
exactly foreseeable. One (or some) of these alternatives had more 
advantageous consequences than all the rest. The right strategy 
was therefore a matter of calculation, followed by the choice of the 
alternative which calculation had proved to be best. 

Since then, we have by degrees moved into situations which are 
not so starkly black and white. The reach of calculation has become 
shorter, and we have had to venture beyond its limits and to take 
chances. Words like "chance" and "random" have begun to appear 



Science as Foresight 415 

in my description of the machines themselves; in situations of such 
limited foresight, the machine or procedure can neither explore nor 
decide infallibly. 

But to stop there would be to encourage a very dubious belief, the 
belief that "chance" and "probability" are words only for our present 
ignorance. It is certainly true that we have to introduce the idea of 
"chance" at the point where our foresight meets a check, and exact 
calculation can advance no further. But we must not suppose that 
this breakdown is our fault, and that a more penetrating eye might 
see to the end, and a more patient machine might calculate beyond 
probability to certainty. This was indeed believed by scientists in the 
last century, almost as an article of faith; and they looked on science 
as a continuous refinement of calculations which, at any given time, 
were limited only by practical and temporary blocks. But the present 
century has shown that this belief is out of keeping with some known 
facts (in atomic physics, for example, and more remotely in mathe- 
matical logic) . We must believe that probability is not a fiction which 
will shrink from generation to generation until it vanishes, but is in 
places an irremovable element in the formulation of scientific laws. 

i) Games Based on Chance 

It would therefore be wrong to let our analysis rest at machines 
whose reach or foresight is limited simply by practical difficulties 
the difficulty, in practice, of calculating the exact run of a set of 
billiard balls, or of seeing fully more than five or six moves ahead in 
a game of chess. For we also face, in life and in science, situations 
in which decision by calculation, in the classical manner, is not 
merely difficult but is essentially impossible; and where, nevertheless, 
decisions have to be made. 

The obvious examples are games of chance obvious, and by no 
means negligible. The theory of probability, and with it all actuarial 
and insurance work, as well as much genetics and atomic physics, 
spring from the inquiry of gamblers. Galileo first solved a problem 
on the fall of dice for an Italian nobleman; and a French noble, the 
Chevalier de Mer6, put to Pascal a more difficult question on gam- 
blers' stakes which set mathematicians thinking about probability. 

Suppose, then, we begin with a game based on the simplest 



416 What Is Science? 

chance: a game in which you toss a silver dollar, and I call "heads" 
or "tails." I want to make this a fair game, and since I believe that I 
am free to call "heads" or "tails" as I choose, I will leave you equally 
free to control the fall of the dollar, by any sleight of hand you have. 
You can therefore make your dollar come down "heads" or "tails," 
as you choose. Then what is your best strategy, and what is mine? 

Your best strategy is not to use the choice you have, but let the 
dollar fall as it chooses, with no influence from you. For suppose 
you make your throws follow some system; suppose you throw more 
"heads" than "tails," or now and again throw runs of "heads" and 
runs of "tails." By analyzing the sequence of "heads" and "tails" 
you throw, I shall discover your system, and shall call more "heads" 
myself, or (in the second case) call "heads" and "tails" in runs; and I 
shall then win. 

In the same way, if I initially have any bias in my calling (and 
most people have), you will detect it and exploit it, and I shall lose. 
That is, my best strategy also is to call at random and not in any 
orderly way. In fact, if I am wise, I will keep a dollar of my own be- 
hind my back and call according to its (undetectable) whims, rather 
than risk my own more transparent ones. 

This may seem a trifling example and the strategy self-evident. Yet, 
in fact, it contains many hidden assumptions, and the strategy de- 
pends on these. For instance, you and I have naturally assumed 
that when I call right, I win, and always win a dollar; and if I call 
wrong, you win a dollar. If we vary these conditions (for instance, if 
we give bonuses for runs of right or wrong calls), our strategies will 
have to be changed. 

Let me illustrate this. Suppose I still get a dollar when I call right; 
but when I call wrong, I pay a dollar and a half if my call was 
"heads," and only 50 cents if I called "tails." This does not look like 
a very different game, and may even strike you as fair. But it is not 
fair; this is a game at which (with average luck) I can win money. 
By what strategy? 

It is of course obvious that my strategy should be to call "tails" 
more often than "heads," since this reduces my risk of loss. How 
much more often? The answer is that my best strategy is, in any 
eight calls, to call on the average five "tails" and three "heads." If 



Science as Foresight 417 

you cautiously toss all "tails," then my eight calls will give me a 
profit of 50 cents; and if you boldly toss all "heads/' I still make a 
profit of 50 cents. So it does not matter what mixture of "heads" and 
"tails" you choose to throw, and in what proportions, I will (except 
for bad luck) average 50 cents profit on any eight calls. 

I said that I must call five "tails" and three "heads" on the aver- 
age; and this is important. I must still be scrupulous not to have any 
order or system in my calling; you must never know what I am going 
to call next. I must call "heads" and "tails" by chance, only arrang- 
ing that the chances now are not equal but are three to five. For ex- 
ample, I must not call steadily in groups of eight calls, in such a way 
that there are exactly five "tails" and three "heads" in each group. 
For if I did this, you would always know what my eighth call was to 
be (and sometimes the seventh, sixth, fifth, and even fourth as 
well); and since this knowledge would allow you at the least to win 
50 cents on the eighth call, the game would turn from a win for me 
into a win for you. 

ii) Larger Choices 

We need not confine the choice of calls or moves, or of strategies, 
to two. In principle, any game (most simply between two players) in 
which the loser pays the winner, has a best strategy of this mixed 
kind. If the game is so dull as to be fair, this strategy at least assures 
its user (with average luck) that he will not lose. 

As an example, Diagram 11 shows a simple form of the Finger 
Game. This is an elegant and difficult game which does not even 
require a box of matches, and it is recommended to all. As Diagram 
11 shows, the best strategy is unexpected, and hardly likely to be 
guessed by an unmathematical player. 

iii) Minima* Strategy 

The reasoning which lies behind these mixed strategies is straight- 
forward. I scrutinize each of my lines of play or strategies and every 
possible mixture of them. Against each I write the maximum loss 
which you might inflict on me, if you knew in advance that this was 
to be my general strategy. Then I choose that mixture which mini- 
mizes my possible maximum loss. This is the best strategy for me; 



418 What Is Science? 

DIAGRAM 11 

The Finger Game 

The two players move simultaneously. Each shows either one or 
two fingers, and at the same time guesses whether his opponent is 
showing one or two fingers. If both players guess right, or both guess 
wrong, no one pays. If only one player guesses right, he wins from the 
other as many dollars as the two players together showed fingers. 
Thus each player has the choice of four courses: 

(a) to show 1 finger and call 1, 

(b) to show 1 finger and call 2, 

(c) to show 2 fingers and call 1, 

(d) to show 2 fingers and call 2. 

If his call is right and his opponent's wrong, then course (a) will 
win two dollars, courses (b) and (c) will win three dollars, and course 
(d) will win four dollars. 

The game is fair, but a player who knows the right strategy will 
(with average luck) win against one who does not. The right strategy 
is to ignore courses (a) and (d), and to play courses (b) and (c) in 
the ratio of 7:5. That is, the right strategy is, 

in any 12 calls, 

show 1 finger and call 2 

on the average 7 times, and 

show 2 fingers and call 1 

on the average 5 times. 

This strategy is unlikely to be guessed by a gambler who plays hunches. 



and if the game happens to be biased in my favor, my loss on this 
strategy will actually be fictitious it will be a gain. 

This principle, of minimizing my maximum loss, or minimax, has 
wide application. (There is a parallel principle of maximizing my 
minimum gain, which is called similarly the maximin principle; but 
the two principles differ only formally.) It is useful in warlike, 



Science as Foresight 419 

economic and even, in a sense, moral situations. It can be applied 
to all those problems of traffic control, production, provisioning and 
organization which are usually called (linear) program problems. At 
bottom, the principle is a principle of insurance, designed to mini- 
mize over-all risk where (and this is essential to our thought) it is 
impossible to foresee which of a number of alternative risks we may 
meet. 

iv) Scale of Values 

Yet the minimization of risk is itself a very limited approach to 
life; you might think it an old maid's approach. Why play "heads" 
and "tails" at a dollar a toss at all if I am instantly going to retreat 
into a safety play which will ensure me a cautious 50 cents average 
every eight throws? This question is not foolish, but it does not go to 
the root of the matter. If I am playing to win money, and every 
cent equally is money to me, then the minimax strategy I have 
given is incontrovertibly the best. If you find it deficient, that is be- 
cause there is in your mind some other reason for our playing, some 
value which is not measured in equal cents. If this is so, it is no use 
our calculating in cents; we ought to look at the possible wins and 
losses of the game again, in terms of the values which really underlie 
our interest. We ought to attach a special pleasure value to wins 
against the odds, if that is what we feel; or if small sums do not 
interest us, we ought to write them off in an appropriate scale. Pro- 
vided the losses of one of us still become the gains of the other, we 
can revalue the game, and find the best strategy on this scale of 
values. It will be a minimax strategy, but so far as is possible, it 
will yield the satisfactions which really underlie our game occa- 
sional long-shot wins, or big gains, or whatever we really think we 
play for. 

In short, when we criticize the result of a minimax policy, our 
dissatisfaction is not with the arithmetic or even, at bottom, with the 
principle; it is with the scale of values on which we marked the wins 
and losses. You cannot in the end get sensible answers, even in eco- 
nomics, unless you consider the meaning of the values which are 
to be exchanged: for example, whether the marginal dollar really 
means as much to you as the first dollar you earned. No theory of 



420 What Is Science? 

science, and no theory of life, is complete until it has looked at the 
underlying units with which we are working. 



5. Organization and Information 

I have for some time been using words like "chance" and "ran- 
dom/' and have contrasted them with the ideas of a "system" and 
"order." This contrast is central to much of modern thought, in sci- 
ence and outside it, and I want to look at it closely. 

i) Signal and Noise 

Suppose that you are on the lookout for some definite signal or 
instruction let us say that you are driving along a highway, and you 
are looking for a signpost which will tell you where to turn off it. This 
signal usually has a certain strength; that is, at dusk, when you drive 
home, you can usually see the signpost when it is two hundred yards 
away. At this distance, you are in no danger of missing the signpost. 
You do run this danger, progressively, as the strength of the signal 
drops, that is, as the early evening light grows fainter. (If the signal 
strength becomes too weak, you will have to increase it by adding to 
the light reflected from the signpost; you must turn on your head- 
lights.) 

This may seem to be the only danger: that the signal will be too 
weak to be seen in time. But the first time that there is fog about, 
you realize that there is a second danger: the danger that the signal 
does not make sense, because the signpost is not recognizable in 
time. Because of the fog, you may have left for home in good daylight, 
in which the signpost would otherwise be visible for miles. The light 
is now scattered by the fog, but even so, there is as much at two 
hundred yards from any object as there usually is at dusk. Yet you 
cannot see the signpost at two hundred yards, because the irregular 
scattered light blurs the outline of things and loses them in the gen- 
eral haze. 

The orderly or systematic shape that you are looking for, the sign- 
post or signal, has been swamped by the random scattered light. 
The absolute strength of the signal is still great enough, but its 



Science as Foresight 421 

strength relative to the background of disorderly scattered light is no 
longer enough to distinguish signal from background. 

The situation is not improved by adding to the total light, because 
this amplifies the background as well as the signal, and does not im- 
prove their relative strength. You do not, in fact, see better in a fog 
by turning on your headlights; you see worse. To see better in a fog, 
you should cut down the total light which reaches you; you should 
wear dark glasses. Drivers of automobiles often think this incredible, 
because it diminishes the light which can reach them from the sign- 
post they are looking for. It does; but it also cuts down the scattered 
light, and in doing so it can improve the receiver's response to the 
ratio of signal to background, and make the signpost distinguishable. 

The state of affairs which I have been describing is universal. 
Light is scattered more in a fog, but it is scattered always. (Since 
blue light scatters more than red, the sky looks blue; as John Tyndall 
said, "we live in the sky, not under it.") There is a random back- 
ground to everything we do, and whatever sense we are using. When 
we listen to talk, to the radio, on the telephone, we have to filter 
what is meaningful, the signal from the background noise. Indeed, 
this is so general an example that all background scatter is often 
called "noise," and the relative signal strength to background scatter 
is simply called the signal-to-noise ratio. 

And this distinction, between signal and noise or background, 
between the systematic and the randomly scattered, between the 
steady trend and the fluctuating variations, underlies all our actions 
and, with them, our machines and devices. 

ii) The Noisy Line 

In the presence of irregular noise, a signal can never be read with- 
out ambiguity: even if it happens to have reached us with no distor- 
tion, as it were through a gap in the noise, we do not know this at 
the time. Nor can we grow certain of the signal by having it con- 
firmed; for however often it is repeated, there remains the lingering 
doubt that noise has by chance played the same trick each time, and 
again turned into "yes" a signal which was meant to say "no." 

We cannot be certain of the signal, by repetition or other means; 
and yet, we can be certain enough. This is an important idea in sci- 



422 What Is Science? 

ence as in practical life. We accept a signal for what it intends and 
act on the instruction it carries, at something short of certainty. The 
shortfall is a measure of the risk we take, and must take, if we are to 
act at all. If the action is critical, we can reduce the risk by stipulating 
a greater confirmation, and therefore a smaller shortfall. But some 
shortfall we must fix on and accept. Even a thermostat or an auto- 
matic pilot will not work if we ask it to reach perfect equilibrium; 
for then its oscillations, as it hunts for perfection, will always take it 
into an unstable tremor. To be stable, the machine must have some 
roughness or tolerance: it must accept as equilibrium all states which 
fall short of it by not more than some chosen margin. 

What is true of a single signal is true of a sequence or message. 
Consider a sequence of symbols sent over a telegraph line in one 
minute, or punched along one foot of tape; and suppose that this se- 
quence carries an amount of instruction or information I. The mes- 
sage, however, suffers some distortion: there is noise on the line, or 
the tape reader makes occasional errors. As a result, an amount of in- 
formation i is lost, and only 

I-i 

is effective. This effective amount I i can sometimes be increased 
(per minute or foot) by choosing a better system of arranging or cod- 
ing the message; thus the possible systems will determine a 

maximum of (I -i), 

which is the absolute capacity of the noisy line per minute, or of 
the tape reader per foot of tape. 
But this capacity, 

maximum of (I i), 

can only be approached; it cannot in general be reached. For what 
do we mean when we say that the amount of information i has been 
lost? We mean that a man who knew both the message and the er- 
rors would have to provide an amount of information i in order to 
correct the errors. But he would have to provide it directly, as it were 
in person; he could not send it along the same line, or through the 
same tape reader, without further loss. 



Science as Foresight 423 

Once again, in the presence of noise, we cannot expect to reach 
the absolute capacity of the line, without errors. All that we can do 
is to make the average number of errors (per minute or foot) smaller 
than some acceptable tolerance. 

iii) Redundancy 

One way of reducing the surviving errors is to repeat the signal. So 
telegraph companies usually repeat numbers and names; and the 
sender himself repeats critical words, for (as he would explain) he 
does not, repeat not, want to risk a misunderstanding. In the same 
way, the instruction tape shown in Diagram 5 uses for its basic sym- 
bols not single holes but pairs of holes. The machine stops if it 
meets a single hole, and this is a safeguard against errors made in 
punching the tape. 

Repeating a signal is appropriate when, as in these cases, it largely 
stands apart from the rest of the message. More often, the symbols 
or parts that make up a message are linked among themselves. This 
linking makes the symbols partly redundant and thereby provides a 
check on the accuracy of the message as it is received. 

For this reason, every code has some overlap or redundancy. That 
is, its symbols do not all add their full weight of instruction, and 
instead they add confirmation. The letter "u" after "q" in English is 
entirely redundant; the letter "h" after "w" often is; and so are many 
doubled letters. We could write most words (as Bernard Shaw 
wanted us to do) unmistakably with fewer letters, and most sen- 
tences in fewer words. But what we would gain in paper we should 
lose in internal confirmation. 

Redundancy is itself a loss of information: we are packing less 
into a minute or a foot than we could with the same symbols. We 
try to make this voluntary loss match (on the average) the loss 
imposed by the expected noise. We can in fact approach the absolute 
capacity of a line, to any tolerance we fix, by putting our messages 
in a code whose redundancies are appropriate to the form of 
noise. The redundancies then show up, and allow us to correct, all 
but an acceptable proportion of the errors. That is: redundancy 
gives the code a structure or skeleton, which resists the distortion of 
its individual symbols. 



424 What Is Science? 

iv) Information in a System 

When we say that a message carries information, we mean that it 
gives instruction; for example, it may be punched on a tape and tell a 
machine what to do. (In the same way, some philosophers hold that 
the meaning of a word or phrase must be defined as its use the 
instructions which it gives and the contexts in which it does so.) 
Therefore the information lies not in this message or that, but in the 
whole system or code of instructions. The information lies in the 
totality of messages which the system can form. 

In some sense, then, the information in the system or code can be 
measured by the number of messages which it can form (say, per 
foot of tape). It is convenient to count this number not directly, but 
in multiples of two. That is, we say that the information is increased 
by one unit when the system is made able to form twice as many 
different messages (per foot of tape). The reason for choosing this 
scale (a logarithmic scale) can be seen by looking at Diagram 2. 
The counter shown there is in effect a simple device for forming 
messages, in a code of O's and 1's (or dots and dashes). When it has 
two circuits or units, it can form four messages; when a third circuit 
is added, it can form eight; and each unit which is added doubles 
the number of messages again. 

The number of possible messages is a measure of information, in 
this way, when all are formed equally often. But most systems use 
some symbols and form some messages more often than others; and 
allowance must be made for this. We ought to count, not the totality 
of messages, but the totality of choices open to us among them. 

v) Information and Entropy 

How does any one message contribute to the total of information? 
Not by its length and not by its ingenuity, but by its scarcity. A 
message which occurs again and again is expected; it tells us little 
that we did not anticipate, and like the words "the" and "which," it 
adds little that is specific to the instruction. By contrast, a message 
which occurs seldom, such as an SOS, tells us something unexpected 
and new and is highly specific in its call for action. 

If the relative frequency of these two messages is pi and /> 2 , their 



Science as Foresight 425 

scarcity is I/pi and l//>2; so that, on the logarithmic scale which we 
have proposed, their information contents are log 1 /pi and log 7//> 2 
(where the logarithms are calculated to the base 2). In any foot of 
tape, however, there will be (on the average) pi messages of the first 
kind for every p 2 messages of the second. Hence the information 
contributed by the two kinds of message is 

pi log I/pi + p 2 log l/p 2 . 

Similarly, if there are n possible messages in all, whose relative fre- 
quencies are 



we measure the information I in the code or system (per average 
foot) by 

PI log I/pi + p 2 log l/p 2 + . . . + pj log 1/pj + . . . + p n log l/p n . 

This formula agrees with the measure we proposed when the 
messages were all equally frequent. For example, for the counter 
shown in Diagram 2, there are four equally frequent messages; that is, 

PI = ?2 = PS = ?4 = J4, 
so that 

log l/p t = log l/p 2 = log 1/ps = log l/p 4 = 2, 
and the amount of information 

Pi, log I/pi + P2 log l/p 2 + p 3 log l/p 3 + ?4 log l/p 4 

is 2 units. 

The formula for the amount of information I is precisely that for 
the entropy of a physical system which can occupy n possible states 
(with the relative frequencies given). The more nearly equal are the 
frequencies, the larger is the information or entropy, and the smaller 
the redundancy; and (in a physical system) the less useful energy 
can be drawn from the system. Thus entropy is, in a sense, the 
opposite of available energy as I remarked at the outset that in- 
formation is the complement to energy. For example, the Second Law 
of Thermodynamics states that the entropy of a closed physical 



426 What Is Science? 

system always increases; and this means that in any self-contained 
part of the universe, the available energy is running down. 

vi) Organization in a Code 

I have not given these formulae because they have an interest in 
themselves; they have not, and even their practical usefulness is small. 
Their real interest derives from the quantities which occur in them 
and from the way these are put together. 

The quantities are frequencies, and they bring home to us that the 
organization of a code is statistical. This was clear when the redun- 
dancies of the code were designed to combat irregular noise. But 
even in the absence of noise, the code (to approach the capacity of 
the line) must be statistically appropriate; it must match the relative 
frequencies of the instructions which will be sent. The everyday mes- 
sages must be short and the rare messages long, so that the informa- 
tion in each foot or minute remains as near its average as possible. 

For this reason, expressive codes move away from a mass of special 
symbols (some with a small, some with a large content) toward a few 
simple symbols which carry information by their arrangement. This 
is the progress of written language from hieroglyphics or ideograms to 
letters, and from letters to Morse's code of dots and dashes. The 
writing of numbers first in Roman numerals, then in an "alphabet" 
of ten digits, and then only with the symbols "1" and "0," shows the 
same movement. 

That is, the information rests in the arrangement. What we meas- 
ure essentially is the organization of the messages not the meaning 
of individual symbols, but the structure of the whole. This is the 
most important thought in the theory of information. In whatever 
way we seek or exchange information about the world, we do not 
seize its underlying units themselves: what we learn is always about 
their organization. When in science, or in life, we analyze experience 
into parts, the meaning that we reach for lies not in the parts but in 
the structures which they form. 



Science as Foresight 427 

6. The Logic of Science 

I closed my description of machines by saying that they mimic two 
gifts of the mind, deduction and exploration; but that, so far as we 
can see, there remains a third gift still to be understood. Since then, 
I have been laying out the tools for this understanding. It is time that 
we come to grips with it. 

i) Insight and Foresight 

When we watch a subtle act of anticipation, on the football field or 
in the design of an experiment, what strikes us is its individuality. It 
is neither a deduction nor a habit but something more unexpected 
than either; it belongs, in an exact way, to the man and the situation. 
The man has grasped the situation, has seen into it and solved it, by 
an act that goes to its heart. 

That is our feeling, and it plainly appreciates something important. 
Men do not act only in ways which have already been used. They 
invent; they make a new interpretation of events. And the methods 
which they invent are based on their interpretation. 

All living things act to anticipate the future; this is what chiefly 
distinguishes them from lifeless things. But not all methods of 
foresight are the same. Man has evolved a foresight based on the 
interpretation of events. He seeks to anticipate the future, not merely 
by responding to the present, but by understanding it. This is his 
characteristic method, the method of foresight based on insight; and 
he uses it systematically in science. 

ii) Likeness 

We are all aware of this special approach to foresight, which makes 
the difference between a stampede and a gale warning, between a 
homing pigeon and a guided missile. We know what we mean when 
we say that someone proceeds by seeing into and understanding 
events. Yet how docs he proceed? What tools has he for looking be- 
low the bare happening, to reveal something which seems more uni- 
versal? 

Man has only one means to discovery, and that is to find likenesses 



428 What Is Science? 

between things. To him, two trees are like two shouts and like two 
parents, and on this likeness he has built all mathematics. A lizard is 
like a bat and like a man, and on such likenesses he has built the 
theory of evolution and all biology. A gas behaves like a jostle of 
billiard balls, and on this and on kindred likenesses rests much of 
our atomic picture of matter. 

In looking for intelligibility in the world, we look for unity; and 
we find this (in the arts as well as in science) in its unexpected 
likenesses. This indeed is man's creative gift, to find or make a like- 
ness where none was seen before a likeness between mass and en- 
ergy, a link between time and space, an echo of all our fears in the 
passion of Othello. 

So, when we say that we can explain a process, we mean that we 
have mapped it in the likeness of another process which we know to 
work. We say that a metal crystal stretches because its layers slide 
over one another like cards in a pack, and then that some polyester 
yarns stretch and harden like a metal crystal. That is, we take from 
the world round us a few models of structure and process (the parti- 
cle, the wave, and so on), and when we research into nature, we try 
to fit her with these models. 

in) Analysis into Units 

Yet one powerful procedure in research, we know, is to break down 
complex events into simpler parts. Are we not looking for the under- 
standing of nature in these? When we probe below the surface of 
things, are we not trying, step by step, to reach to her ultimate and 
fundamental constituents? 

We do indeed find it helpful to work piecemeal. We take a se- 
quence of events or an assembly to pieces : we look for the steps in a 
chemical reaction, we carve up the study of an animal into organs 
and cells and smaller units within a cell. This is our atomic approach, 
which tries always to see in the variety of nature different assemblies 
from a few basic units. Our search is for simplicity, in that the dis- 
tinct units shall be few, and all units of one kind identical. 

And what distinguishes one assembly of these units from another? 
the elephant from the giraffe, or the right-handed molecule of sugar 



Science as Foresight 429 

from the left-handed? The difference is in the organization of the 
units into the whole; the difference is in the structure. And the like- 
nesses for which we look also are likenesses of structure. 

This is the true purpose of the analytic method in science: to shift 
our gaze from the thing or event to its structure. We understand a 
process, we explain it, when we lay bare in it a structure which is like 
one which we have met elsewhere. 

iv) Finding the Units 

This method at once recalls my description of the theory of infor- 
mation: the different assemblies are, as it were, different messages 
constructed from the same alphabet of units. And the analogy would 
be convenient, but for one defect, which is critical. In science, we do 
not know the units in which the "messages" are written. We have to 
find them. 

Leibniz long ago described the procedure of science as like the 
solving of a cryptogram; and this is a deep and an exact remark. In a 
scientific research, we have to do the opposite to transmitting infor- 
mation, so that we have to turn the theory of information back- 
ward. Instead of sending messages in a known code, we receive 
messages in an unknown code. The aim of science is to break the 
code of nature. 

This is evident in any practical example. One of the characteristics 
of science is that it tries to put its descriptions of nature in a 
mathematical form. Mathematical formulae, of course, display the 
arrangement of coded messages most clearly. Thus when Isaac New- 
ton in 1687 formally set out the laws of motion, he was (in the 
language which I have been using) writing the basic messages of 
which all mechanics is a rearrangement. And such a message as 



(applied force equals mass times the resulting acceleration) does not 
arrive from nature ready-made. On the contrary, it has to be puzzled 
out from an apparently meaningless multiplicity of everyday observa- 
tions and experiments, and the puzzle is to find the units which 
matter within these. Newton's genius was precisely this, that he dis- 



430 What Is Science? 

entangled the units and showed that the observations made sense if 
they were expressed in them. He set out what was happening in 
terms of force and mass and acceleration, and for this purpose he and 
those who had come just before him (particularly Galileo, who 
died in the year 1642 in which Newton was born) had to invent 
such concepts as force and mass. 

What is mass? Newton did not really define it, and even now, when 
the general theory of relativity has healed a great duality (between 
inertial mass and gravitational mass, that is roughly between mass 
and weight), we are still remote from understanding the nature of 
mass. What is force? The theory of relativity has undermined the 
concept of force altogether, but even before this, its standing had 
been uncertain. And in fact, the concepts of mass and force were 
never independent, but defined one another indirectly by the for- 
mula I have just written, in which only the acceleration / is fairly 
directly measurable. 

In short, mass and force are not in any definable sense real entities, 
discovered by turning a microscope on nature, and there seen mani- 
festly to cause her behavior. They are concepts whose isolation makes 
the behavior of nature orderly. In discovering these concepts, Galileo 
and Newton were not making a statement of fact. They were finding 
units of a code, an alphabet in which mechanics could be written 
coherently and consistently. The formula I have written is one of its 
basic messages, and what is important in it is not the fact but the 
discovery of the code. 

v) The Implication of a Code 

We can see the same thought at work, the search for the key to a 
cryptogram, wherever a science has had to go forward to frame a new 
concept. John Dalton worked in the same way when, in 1808, he 
proposed that chemical action is a linking of atoms with atoms. So 
did Louis Pasteur when, in 1848, he related some chemical differ- 
ences to the right-handed or left-handed structure of crystals. Such 
discoveries as the benzene ring, the electron, and insulin, all followed 
the same thought. Diagram 12 shows in outline a characteristic 
progression of decoding in science, and the new concepts implied at 
each step, 



Science as Foresight 431 

DIAGRAM 12 

Scientific Theories as Decoding 



The action of what was then called oil of vitriol on common salt 
was known to Dr. Johann Rudolf Glauber in 1648. But only in the 
last century did this and other chemical reactions fall into place, and 
become a connected system of messages, by being written out in 
their elements: 



H 2 SO 4 + ZNaCl -> Na 2 SO 4 + 2HC1. 



The units or symbols in this code are the (concepts of the) atoms 
of the 92 natural elements. 

Next, chemists began to ask why S is so often coupled with O 4 , 
and why the letter II moves about in so many of these messages. This 
is the familiar step in decoding which counts the frequencies of letters 
and groups. Here it leads to the theory of valency and the concept of 
chemical bonds. 

By analyzing in the same way sentences in which physicists record 
their experiments, we group these bonds round new concepts: the 
physical atoms. At this stage, each atom has a nucleus round which 
are arranged electrons in shells. Thus the symbols II and O and S 
are being further broken up, each into an unknown nucleus and a 
characteristic (atomic) number of electrons. 

Since 1932, the nucleus in turn has been analyzed into unit concepts 
the proton and the neutron. Thus all atomic and nuclear reactions 
are written (in their essential skeletons) in a four-symbol code: e~~ 
for the ordinary electron, e+ for the positive electron, p+ for the 
proton and n for the neutron. When letters H, O and so on are still 
retained for the elements and their isotopes, it is merely as familiar 
and useful contractions. 

For example, one of the two processes by which hydrogen is fused 



432 What Is Science? 

DIAGRAM 12 continued __ 



to form helium in the sun, in three steps, is written (in its essential 
skeleton), 



(p+n) +p+- (p+p+n), 
(p+p+n) + (p+p+n) -* (p+p+nn) + p+ + p+; 

in which (p+n) is a heavy isotope of the hydrogen nucleus, and 
(p+p+n) and (p+p+nn) are two isotopes of helium. 

So, step by step, the concepts or units in the code of nature grow 
fewer, and her meaning is carried by their arrangement. 

vi) The Use of Experiments 

Plainly it is stimulating to think of the discovery of new scientific 
concepts thus, as the unraveling of a coded puzzle. But we naturally 
ask, how do we set about it? What procedure have we which will 
ensure that we find the code? 

The answer is, none. As in all cryptography, there is no process 
which is certain to break the code. But as in all cryptography, there 
are systematic methods which are likely to help. In science, there is 
one most powerful method: we can add to the stock of coded mes- 
sages on which we have to work, by doing further experiments. This 
method is seldom open to the cryptographer, and never to the histo- 
rian; they have to take the messages they have, and be thankful. 

The sciences, however, do not have to make do with the observa- 
tions of nature as they come. They are able to ask questions of na- 
ture, to which she replies in the same code. That is, they can do 
experiments, and add the new results to the observations they already 
have. They can do this even in so inaccessible a subject as astronomy, 
if they think out their experiments on earth appropriately. Christian 
Doppler in 1842 learned from the whistle of a locomotive that a 
receding star should also change the pitch or wave length of its light. 
And today the big nuclear accelerators (and the big calculating ma- 
chines) are used to see whether our theories of the evolution of the 
stars fit and hold together. 

For the strength of the scientist is that he can choose the experi- 
ments he makes. Like a cryptographer who has captured an enenrw 



Science as Foresight 433 

agent, he can send searching signals which are designed to evoke 
simple and decisive answers. This is the function of the well- 
planned experiment: to isolate one possible concept from the rest, 
and thus to get results which establish decisively that one unit or 
symbol enters in the messages of nature in a specific way. 

Experiments, then, are questions which we put to nature in order 
to add to the stock of messages from which we must decipher her 
code. But since we can choose the questions, we can design them to 
get particularly simple replies, which make the task of decoding less 
haphazard. This is why the experimental sciences have been so much 
more successful in finding unifying concepts and results than have 
other human speculations. 

vii) The Test of Induction 

The theory of information is like the logic of deduction: it begins 
from accepted general principles, and can then go forward step by 
step, with no false starts and returns. But the discovery of scientific 
concepts turns the processes of information backwards, as induction 
turns deduction backwards; and like induction, it is not unique. It is 
in fact an extension of induction. 

Induction is the process of generalizing from our known and lim- 
ited experience, and framing wider rules for the future than we have 
been able to test fully. At its simplest, then, an induction is a habit or 
an adaptation the habit of expecting tomorrow's weather to be like 
today's, the adaptation to the unwritten conventions of community 
life. All our conscious acts are based on such inductions, uncertain 
but indispensable; and most justifications of induction are content 
with such piecemeal habits. 

But the striking feature of your behavior or mine is that it is not 
piecemeal: it is of a piece, it makes a coherent personality, it is linked 
and organized within. It is based on concepts of nature and of con- 
duct which have been formed not only by habit but by interpreta- 
tion. Induction in animals may be nothing but habit, which antici- 
pates the future mechanically as a copy of the past. But human 
beings base their foresight on understanding, that is (we now see) 
on forming concepts and joining them into structures which are 
simple models of the world. 



434 What Is Science? 

In intelligent human behavior, therefore, the test of induction is 
not simply whether it accords with past experience. Many alternative 
ways of expecting the future will do that; induction is never unique. 
How are we to choose among these alternatives, each of which will 
equally fit what has happened in the past? 

In my view, we choose the alternative which best organizes our 
total experience. Let me put this precisely, and for this purpose let 
me return to scientific rather than everyday behavior. We have, then, 
a collection of facts or experiments, by which I mean processes with 
known results. We think of each of these as a message which goes 
forward in time, from left to right, saying what we start with and 
what then happens. These messages are in an unknown code. We 
propose a code and examine the messages. Some of them now are 
implied by the remainder and say nothing new; we discard these. The 
rest form a system of basic messages assembled from the code sym- 
bols. We can measure the information content of these messages as 

pi log 1/p! + p 2 log l/p 2 + .... + pj log 1/pj + .... + p n log l/p n , 

as we learned to do for any messages made up of known symbols. The 
total content of information of the system of basic messages in this 
code can therefore be calculated. 

Then if we have a choice of codes which otherwise accord equally 
well with our experience, we prefer the code which gives the highest 
content of information. We have, in fact, one object in looking for 
concepts in nature: to unify her, make her orderly and, in this sense, 
meaningful. Therefore the concepts or code symbols which we prefer 
are those which make our experience more orderly and connected 
than others. We try to maximize the meaning that we can find in 
nature. 

viii) Conclusion 

I have taken a wide survey of man's intelligent activity, specifically 
as it is displayed in the methods of science. It may seem odd to have 
done this by looking at machines and at games of strategy. My reason 
is that these mechanisms embody most clearly the formal procedures 
we know for looking toward the future. 

The first of these procedures is that of deductive logic. It is seen 



Science as Foresight 435 

in all calculating machines, which are today largely logical machines. 
They can give us new courage in tackling problems which are too 
complex for isolation and experiment, say in economics and social 
science. And their approach there is interesting, because it does not 
begin by making a simplified model of the process. It accepts all the 
data, and searches them for all correlations. 

These logical machines can be made to run a chemical factory, to 
choose the winning move in a chess problem, to translate a simple 
text, to put together a reasonable debate or sonnet. This kind of 
machine has always fascinated men, long before it rode into the 
comic strips. When Charles Babbage in the 1830s was building his 
pioneer machine, complete with automatic instructions and memory 
(a hundred years before his time), the paleontologist Thomas Haw- 
kins wrote that his friend John Clark had in mind another 

extraordinary machine which he was constructing: one that makes 
Latin verses no two alike for ever, all of them quite grammatical 
and of pure sense. 

Machines of this kind can be enlarged to explore alternative 
courses, to feed back the results of their actions, and accordingly to 
correct themselves. They can even be made to learn from this process, 
by incorporating the correction permanently into their program of 
action. But in doing so, the machine becomes more and more an 
adaptive rather than a deductive mechanism a biological rather than 
a physical model, whose procession is more like that of evolution 
than like, say, a planetarium. This kind of machine is best made of 
many unit elements and circuits, with random connections, and with 
single on or off, yes or no decisions based on chance. It is particularly 
suited to exploring a changing environment and will of itself find 
adaptations which, while stable in the largest sense, respond delicately 
to small changes. 

These two kinds of machine display two kinds of foresight. There 
remains, in my view, a third kind, which is characteristically human. 
This is the wish to base foresight on insight. It seeks to understand 
nature by looking for unifying and simplifying concepts. I have 
shown that, on this view, the processes of nature can be pictured as 
messages written in a code whose unit-symbols are unknown to us, 



436 What Is Science? 

and which are the concepts we seek. We can help our search by 
experiments which are planned to evoke decisive answers from na- 
ture. But there is no automatic procedure for breaking a code and no 
assurance that our way of deciphering it is unique. On the contrary, 
the displacement of one scientific theory by another shows that it is 
not. Nature is more intricately organized and cross-linked than our 
theories, so that each model or likeness that we try scores some strik- 
ing successes and then falls short. All that we can do, at any state of 
our factual knowledge, is to prefer that code which makes what we 
know most orderly. That is, we choose those concepts which organize 
the messages of nature most coherently. We achieve this, in my view, 
by maximizing their content of information or meaning. This is the 
test for the inductions by which we try to generalize from our par- 
ticular experience and to gain a basis for foresight. 
Charles Darwin said sadly at the end of his life that 

my mind seems to have become a kind of machine for grinding 
general laws out of large collections of facts. 

Darwin was too modest. If such a machine can indeed be made, we 
do not know how to make it. Indeed, we do not know anything like 
it, except a man. For the discovery of laws is a complex induction 
like the solving of a cryptogram which, so far as we know, a machine 
procedure can help but cannot complete. It depends on an imagi- 
native act, seeing the structure of the solution in a likeness, and 
seizing a likeness where none was expected. This is the third gift of 
the mind. 



Bibliography 



ANTHROPOLOGY 

GENERAL 

1. Kroeber, A. L. Anthropology. New York: Harcourt, Brace, 1948. 
Not a textbook, but a treatise. Insofar as it can be done between the covers 
of a single book and by one man, Kroeber has synthesized the total theoretical 
and substantive content of anthropology. 

2. Kroeber, A. L. (Editor). Anthropology Today. Chicago: Univer- 
sity of Chicago Press, 1953. 

Fifty specialists survey the state of existing knowledge in most, but not all, 
of the principal fields. Many of the chapters are highly technical, but this is 
an authoritative compendium of present anthropological knowledge. 

3. Beals, R. L. and Hoijer, H. An Introduction to Anthropology. 
New York: Macmillan, 1953. 

A reliable textbook. 

4. Kluckhohn C. Mirror for Man. New York: McGraw Hill, 1949. 

A popular presentation of all branches of anthropology as they relate to con- 
temporary intellectual and practical issues. 

ARCHAEOLOGY 

5. Howells, William, Back of History. New York: Doubleday and 
Company, 1954. 

Skillfully combines archaeology and physical and cultural anthropology, but 
the emphasis is archaeological. Unfortunately lacks a bibliography. 

6. Coon, Carleton S. The Story of Man. New York: Alfred Knopf, 
1954. 

437 



438 Bibliography 

The best up-to-date and popular biography of mankind. A wider sweep than 
Howells' and richer in ideas. 

7. Childe, V. Gordon. Social Evolution. London: Watts and Com- 
pany, 1951. 

This book, by a foremost archaeologist, summarizes some of the main findings 
on Old World archaeology and relates them to the evolution of economy 
and social organization. Childe is a stimulating writer. 

8. Oakley, K. P. Man the Tool-Maker. London: British Museum, 
1949. 

Simple but careful discussion of the antiquity of man, the Paleolithic, and 
early technology. 

9. Clark, J. G. D. Prehistoric Europe: The Economic Base. New 
York: Philosophical Library, 1952. 

A thoughtful and quite comprehensive volume. 

10. Brew, J. O. Archaeology of Alkali Ridge, Southeastern Utah. 
Papers of the Peabody Museum of Harvard University, 1946. 

One of the best monographic studies of North American archaeology with 
incisive treatment of method and theory. 

PHYSICAL ANTHROPOLOGY 

11. Hooton, E. A. Up from the Ape. New York: Macmillan, 1946. 
A good general book on human evolution. 

12. Demerec, M. (Editor). The Origin and Evolution of Man. Cold 
Spring Harbor Symposia on Quantitative Biology, vol. 25, 1951. 

Somewhat technical but authoritative papers by 37 European and American 
anthropologists and biologists. The best single source available on many 
aspects of biological anthropology. 

13. Boyd, W. C. Genetics and the Races of Man. Boston: Little, 
Brown and Co., 1950. 

Racial anthropology from the standpoint of an immunologist and geneticist. 
Good material on methods, especially quantitative. 

14. La Barre, Weston. The Human Animal. Chicago: University of 
Chicago Press, 1954. 

An introduction to human biology from the standpoint of a cultural an- 
thropologist. Not altogether successful, it nevertheless provides what is other- 
wise lacking: a readable account of the intertwining of biology and culture. 

CULTURAL ANTHROPOLOGY 

15. Kroeber, A. L. Configurations of Culture Growth. Berkeley: Uni- 
versity of California Press, 1944. 



Bibliography 439 

The outstanding anthropological study of the great civilizations of the world. 
More modest in scope and in conclusions than Spengler, Sorokin and Toyn- 
bee, it is also better poised and more genuinely scientific. 

16. Benedict, Ruth. Patterns of Culture. Boston: Houghton Mifflin, 
1934. 

A classical and readable introduction to cultural anthropology for the lay- 
man. 

17. Firth, Raymond. Elements of Social Organization. London: 
Watts and Company, 1951. 

A nontechnical treatment with excellent material on economics and art. 

18. Linton, Ralph. The Tree of Culture. New York: Alfred A. 
Knopf, 1955. 

A stimulating treatment of the culture history of the major areas of the 
world. Rich in picturesque detail, bold interpretation, and pleasant to read. 

19. Howells, W. W. The Heathens: Primitive Man and His Re- 
ligions. New York: Doubleday and Company, 1948. 

A good book on primitive religion. 

20. Redfield, Robert. The Primitive World and Its Transformations. 
Ithaca, New York: Cornell University Press, 1953. 

A broad but pointed survey of some of the principal issues in cultural an- 
thropology with particular stress upon values. 

21. Honigmann, John. Culture and Personality. New York: Harper 
and Brothers, 1954. 

A clear synthesis of this new and controversial field. Bibliography will lead 
the reader to the most important sources, whether books or articles in 
learned journals. 

22. Barnett, H. G. Innovation, The Basis of Cultural Change. New 
York: McGraw Hill, 1953. 

A profound study of the anthropological and psychological facts and prin- 
ciples relating to the acceptance or rejection of new things and practices. 

23. Evans-Pritchard, E. E. The Nuer. Oxford: Oxford University 
Press, 1940. 

The recommendation of a single tribal monograph is invidious. However, no 
reading list would be complete without at least one such basic work. This 
study of an African people is outstanding for its soundness of documentation, 
originality and readability. 

24. Dyk, Walter. Son of Old Man Hat. New York: Harcourt, Brace, 
1938. 

It is also essential to get at least one full-bodied picture of the individual in 
his culture. This Navaho Indian autobiography has vividness and immediacy. 



440 Bibliography 



ANTHROPOLOGICAL LINGUISTICS 

25. Sapir, Edward. Language. New York: Harcourt, Brace, 1921. 

This little book is dated in some technical respects, but its succinctness and 
the felicity of its style make it enduring. Both students and laymen will find 
it a pleasure to read. 

26. Mandelbaum, David (Ed). Selected Writings of Edward Sapir. 
Berkeley: University of California Press, 1949. 

About one-half of this book consists of well-known papers on language by 
the greatest of anthropologicalinguists. The remainder of the volume deals 
with culture with a psychological and literary emphasis. 

27. Bloomfield, Leonard. Language. New York: Henry Holt, 1933. 
A standard and admirable textbook, although it lacks some important con- 
tributions of the past two decades. Behavioristic in standpoint. 



MATHEMATICS AND LOGIC 

1. Ball, W. W. Rouse. Mathematical Recreations and Essays, llth 
edition. New York: Macmillan, 1939. 

Packed with information but arranged more as a handbook than for con- 
tinuous reading. Indispensable for anyone interested in puzzles. 

2. Bell, E. T. Men of Mathematics. New York: Simon and Schuster, 
1937. 

A most enjoyable collection of biographical sketches of the leading mathe- 
maticians from Zeno to Poincare'. 

3. Cohen, Morris, and Nagel, Ernest. Introduction to Logic and 
Scientific Method. New York: Harcourt, Brace, 1934. 

An admirable textbook requiring no previous training in mathematics and 
logic. It presents an excellent survey of logic, scientific method, probability 
and related topics and is thoroughly readable. 

4. Hogben, Lancelot T. Mathematics for the Million. New York: 
W. W. Norton, 3rd edition, 1951. 

Not mathematics for the millions but a lively and stimulating survey for 
anyone prepared to use pad and pencil on the hard parts. 

5. Hardy, G. H. A Mathematician's Apology. Cambridge: Cam- 
bridge University Press, 1941. 

A delightful volume of reminiscences by the late G. H. Hardy, one of the 
world's great mathematicians. He examines the nature of mathematics, ex- 
plains why it is worth studying and explores the traits of mind of persons 
attracted to the subject. There is no other book quite like this one. 



Bibliography 441 

6r^ Jourdain, P. E. B. The Nature of Mathematics. London: T. C. 
and E. C. Jack, 1912, and New York: Dodge Publishing Company, 
1912. 

A book of 90 pages, this is one of the best primers of mathematics ever 
published. Jourdain was a talented mathematician and logician. He had wit, 
a clear style and a genuine feeling for popularization. (Out of print but 
included in a new anthology of mathematical literature edited by James R. 
Newman and to be published in 1956 by Simon and Schuster.) 

7. Kasner, Edward and Newman, James R. Mathematics and the 
Imagination. New York: Simon and Schuster, 1940. 

The only popular survey primarily concerned with the higher branches of 
mathematics, such as topology, theory of infinite classes, probability, non- 
Euclidean geometry, the calculus, and the foundations of mathematics. 

8. Kline, Morris. Mathematics in Western Culture. New York: Ox- 
ford University Press, 1953. 

An exceptionally readable account of the contributions of mathematics to 
Western life and thought from the ancient Greeks to the present. Professor 
Kline is an interesting writer and a brilliant explainer of difficult mathe- 
matical ideas. 

9. Titchmarsh, E. C. Mathematics for the General Reader. London: 
Hutchinson's University Library, 1950. 

A lucid, unhurried survey of the science of number, from arithmetic to 
algebra, trigonometry and the calculus. Rewarding even for the reader who 
is unable to follow every argument. 

10. Smith, David Eugene and Ginsburg, Jekuthiel. Numbers and 
Numerals. New York: Teachers College, Columbia University, 1937. 

An authoritative, well-written, attractively illustrated pamphlet which tells 
the story of numbers, how they came into use, what the first crude numerals 
or number symbols meant "in the days when the world was young." 

11. Sutton, O. G. Mathematics in Action. New York: Thomas Y. 
Crowell Company, 1955. 

The director of the British meteorological office, a foremost mathematician, 
presents a clear account of how mathematics is applied to various sciences: 
physics, astronomy, ballistics, aerodynamics, weather forecasting, astronomy, 
etc. It is a feat to cover this enormous field in two hundred-odd pages, but 
Sutton not only succeeds in accomplishing it but in explaining the rudiments 
of higher mathematics to readers without special training. 

12. Tarski, Alfred. Introduction to Logic. New York: Oxford Uni- 
versity Press, 1941. 

The best elementary book in English on symbolic logic. If Whittaker's es- 
say has whetted the reader's appetite for more information on the subject he 



442 Bibliography 

is rortunate to be able to follow up with two such good books as Cohen and 
Nagel and this more specialized volume. 

13. Whitehead, Alfred North. Introduction to Mathematics. New 
York: Oxford University Press, revised edition, 1948. 

Whitehead's book has to a certain extent been superseded by other populariza- 
tions; but it is still worth reading and the flavor of Whitehead's personality 
confers distinction on every page. 

14. Moroney, M. J. Facts from Figures. London: Penguin Books, 
1951. 

An able introduction to statistics for the serious reader. One can learn a great 
deal from Moroney's book, but one must be prepared to follow its mathe- 
matical reasoning which, though taught from the ground up in these pages, 
is not always easy. 

15. Tippett, L. H. C. Statistics. New York: Oxford University Press, 
1943. 

This book in the Home University Library series affords a fine introduction 
to statistical reasoning, without the use of equations or symbols. Recom- 
mended for itself or as a less strenuous companion to Moroney. 



ASTRONOMY AND COSMOLOGY 

1. Hoyle, Fred. The Nature of the Universe. New York: Harper and 
Brothers, 1950. 

A brief description of the modern view of astronomical subjects. Very easy 
to follow. 

2. McCrea, W. H. Physics of the Sun and Stars. New York: Long- 
mans, Green and Co., Inc., 1951. 

An excellent introduction. Thorough, but almost wholly nonmathcniatical. 

3. Johnson, Martin. Astronomy of Stellar Energy and Decay. Lon- 
don: Faber and Faber Limited, 1950. 

An outline of facts and theories about the life history of the stars written 
with a fine appreciation of the problems involved. The book is divided into 
two parts, one for the general reader, one for the more advanced student. 

^ ^ Gamow, George. The Birth and Death of the Sun. New York: 
Viking Press, 1945. (Also in an inexpensive reprint in the New Ameri- 
can Library series.) Also, The Creation of the Universe. New York: 
Viking Press, 1952. 

These two books deal informally and agreeably with modern problems of 
astronomy. The first volume is primarily devoted to stellar evolution and is in 



Bibliography 443 

a few places ?lready out of date. The second is an absorbing presentation of 
relativistic cosmology. 

5. Lemaitre, Georges. The Primeval Atom. New York: D. Van 
Nostrand Company, Inc., 1950. 

The classic nonmathcmatical description of Canon Lemaitre's hypothesis 
of the origin of the universe. A book of charm and fascination. 

6. Payne-Gaposchkin, Cecilia. Stars in the Making. Cambridge: 
Harvard University Press, 1952. 

The Phillips Astronomer at Harvard presents a popular study of all the 
observational clues to the problem of stellar evolution. Dr. Gaposchkin is an 
admirable writer. 

7 Introduction to Astronomy. New York: Prentice-Hall r 

Inc., 1954. 

A superior primer of astronomy: up-to-date, authoritative, rich in historical 
and biographical details. 

8. Struve, Otto. Stellar Evolution. Princeton: Princeton University 
Press, 1950. 

A penetrating but rather advanced study. 

9. Menzel, Donald H. Our Sun. Philadelphia: Blakiston, 1949. 

An unencumbered discussion of surface phenomena on the sun (a subject not 
discussed in Dr. Bondi's essay), with a chapter on the interior of the sun. 

10. Shapley, Harlow. Galaxies. Philadelphia: Blakiston, 1943. 

Dr. Shapley, one of the foremost living astronomers, is a lively writer. Here he 
gives a satisfying account of observational cosmology. 

11. Hubble, Edwin. The Realm of the Nebulae. New Haven: Yale 
University Press, 1936. 

For the scientifically minded general reader, a skillful description of what is 
known about the nebulae. This book is slightly more technical and a little 
longer than Shaplcy's. 

12. Bondi, Hermann. Cosmology. Cambridge: Cambridge University 
Press, 1952. 

Bondi's beautifully succinct description of modern cosmologies is difficult in 
paits, but the thoughtful reader need not stay away. 

13. Whitrow, G. J. The Structure of the Universe. New York: 
Hutchinson's University Library, 1949. 

The emphasis of this interesting book is on the more philosophical problems 
of cosmology and on the historical aspects. ^/ 

14. Eddington, Sir Arthur Stanley. The Expanding Universe. Cam- 
bridge: Cambridge University Press, 1933. 

This popular masterpiece is now slightly out of date but it is enormously read- 
able and still worth reading. Both this book and Whitrow's were written 



444 Bibliography 

before the publication of the steady-state theory; these two, and Bondi's book, 
before the recent redetermination of the distances of the galaxies. 



PHYSICS 

1. Hecht, Selig. Explaining the Atom. (Revised and expanded by 
Eugene Rabinowitch.) New York: The Viking Press, 1954. 

By far the best popular book on atomic energy, explaining with exceptional 
clarity the main features of atomic structure and behavior, the mechanics of 
fission and fusion, the future of atomic power. The late Selig Hecht was a 
brilliant biophysicist who felt deeply the social responsibilities of the scien- 
tist. 

2. Eddington, Sir Arthur Stanley. Space, Time and Gravitation. 
Cambridge: Cambridge University Press, 1920. 

Dated with respect to developments of nuclear physics and other advances 
of the last quarter century, this book by a leading 20th-century physicist and 
a master of popularization remains one of the classic accounts of relativity 
theory and how the new physics differs from the old. An enthralling volume, 
but not easy. 

3. Taylor, Lloyd William. Physics: The Pioneer Science. New York: 
Hough ton Mifflin, 1941. 

An attractive text for a "liberalized course in general physics" at the first 
college level; rich in historical and biographical material. 

4. Lemon, Harvey Brace. From Galileo to the Nuclear Age. Chicago: 
The University of Chicago Press, 1946. 

A clear, entertaining introduction to physics. Fine illustrations. 

5. Crowther, J. G. British Scientists of the Twentieth Century. Lon- 
don: Routledge and Kegan Paul Ltd., 1952. 

Essays describing the lives and achievements of four of the foremost con- 
tributors to modern physics: J. J. Thomson, Lord Rutherford, Sir James 
Jeans, Sir Arthur Eddington. A thoughtful, interesting book by the leading 
British science journalist. 

6. Einstein, Albert and Infeld, Leopold. The Evolution of Physics. 
New York: Simon and Schuster, 1938. 

An able, popular account of the growth of ideas in physics, from the me- 
chanical view of the universe to field theory, relativity and quanta. Not al- 
ways easy to follow but worth the effort. 

7. Frisch, Otto Robert. Meet the Atoms. New York: A. A. Wyn, 
1947. 

Dr. Frisch, a pioneer of nuclear research, provides a lively, well-paced, in- 
formal guide to the essential ideas of modem physics. 



Bibliography 445 

8. Durell, C. V. Readable Relativity. London: G. Bell and Sons 
Ltd., 1938. 

This book is an extraordinary achievement. Step by step, leaving behind no 
unanswered questions, Durell, using only the simplest algebra, explains the 
entire formidable apparatus of relativity, both the special and the general 
theory. If you remember any high-school algebra and want to gain an inkling 
of the mathematical reasoning underlying the most celebrated of modern 
scientific concepts, you will find this book an exciting intellectual adventure. 

9. Dampier, Sir William Cecil. A History of Science. Cambridge: 
Cambridge University Press, 4th edition, revised and enlarged, 1949. 

The standard modern one-volume survey, wholly accessible to the thought- 
ful general reader. Dampier's history covers fully the evolution of physics 
as well as the other sciences and is particularly valuable in exhibiting the 
relations between science, philosophy and religion. 

10. Sedgwick, W. T. and Tyler, H. W. (Revised by Tyler, H. W. 
and Bigelow, R. P.) A Short History of Science. New York: The 
Macmillan Company, 1939. 

Somewhat more elementary than Dampier's book and skimpy on the science 
of the 20th century, but a straightforward, readable history with many ex- 
cellent illustrations. 

11. Cajori, Florian. A History of Physics. New York: The Macmillan 
Company, revised edition, 1929. 

An authoritative work, succinct and not too difficult. 

12. Millikan, Robert Andrews. Electrons (+ and ), Protons, Pho- 
tons, Neutrons, Mesotrons and Cosmic Rays. Chicago: The Univer- 
sity of Chicago Press, revised edition, 1947. 

A noted American scientist describes the development of atomic theory dur- 
ing the last 50 years. Interestingly written, comprehensive, accessible, in large 
part, to a wide audience. 

13. Needham, Joseph and Pagel, William. Background to Modern 
Science. Cambridge: Cambridge University Press, 1938. 

Ten leading scientists explain in popular style the work that led to the scien- 
tific advances of recent times. Recommended especially for the essays on 
physics by Lord Rutherford, crystal physics by W. L. Bragg, atomic theory 
by F. W. Aston, astronomy by Sir Arthur Eddington. 

CHEMISTRY 

HISTORICAL AND CULTURAL 

1. Read, }. Humor and Humanism in Chemistry. London: Bell, 
1947. 



446 Bibliography 

A richly illustrated work of the historical type, with the underlying theme 
that "the study of chemistry, if approached befittingly, may reasonably take 
rank beside the humanities as a broadly educative, cultural and humanizing 
influence. . . ." 

2. . Prelude to Chemistry. New York: Macmillan, 1937. 

A work dealing with alchemy in its multifarious aspects, containing much 
original matter, and copiously illustrated. 

3. Partington, J. R. A Short History of Chemistry. London: Mac- 
millan, 2nd edition, 1948. 

A concise and authoritative account, well documented and containing many 
illustrations. 

4. Findlay, A., Chemistry in the Service of Man. London: Long- 
mans, Green, 1947. 

"Some account of what the science of chemistry, both in its general prin- 
ciples and in its industrial application has accomplished for the material well- 
being and uplifting of mankind." With illustrations. 

5. Jaffe, Bernard. Crucibles: The Story of Chemistry y From Ancient 
Alchemy to Nuclear Fission. New York: Simon and Schuster, Inc., 
revised edition, 1948. 

A fine popular account of the growth of chemical knowledge told through 
the lives of the leading chemists from the 1 5th century to the present period. 

6. Friend, J. Newton. Man and the Chemical Elements. New York: 
Charles Scribner's Sons, 1953. 

The story of the discovery of the various chemical elements: how they were 
sought out, by whom, the uses to which they have been put. A clear account 
with many diverting historical sidelights. 



INORGANIC CHEMISTRY 

7. Findlay, A. General and Inorganic Chemistry. London : Methuen, 
1953. 

A volume in the Home Study Series, planned to provide new interpretations 

of modern knowledge for the layman. 



PHYSICAL CHEMISTRY 

8. Goddard, F. W. and James E. J. F. The Elements of Physical 
Chemistry. London: Longmans, Green, 1954. 
A clear, simple introduction to the subject. 



Bibliography 447 



ORGANIC CHEMISTRY 



9. Read, J. A Direct Entry to Organic Chemistry. London: Methuen, 
1948. 

An excellent volume in the Home Study Series. 
BIOCHEMISTRY 

1. Bacon, J. S. D. The Chemistry of Life: An Easy Outline of Bio- 
chemistry. London: Watts and Co., 1944. 

A popular, readable introduction. 

2. Borek, Ernest. Man the Chemical Machine. New York: Columbia 
University Press, 1952. 

This clear and authoritative book describes for the general reader some of 
the outstanding achievements of biochemistry. 

3. Baldwin, Ernest. An Introduction to Comparative Biochemistry. 
Cambridge: Cambridge University Press, 1949. 

A skillful, attractively written little volume bringing together material widely 
scattered throughout the literature. Sir Frederick Gowland Hopkins, in his 
preface, widely recommends this study of the chemical nature and functions 
of animals to students as well as to those "whose interest may be great but 
their leisure small." 

4. Baldwin, Ernest. Dynamic Aspects of Biochemistry. Cambridge: 
Cambridge University Press, 2nd edition, 1952. 

A first-class textbook of general biochemistry. 

5. Tracey, N. V. Principles of Biochemistry: A Biological Approach. 
London: Isaac Pitman and Sons, Ltd., 1954. 

An excellent book for the serious student about to begin the study of bio- 
chemistry. Though this may be regarded as an advanced work it is very 
readable. 

6. Parsons, T. R. Fundamentals of Biochemistry in Relation to 
Human Physiology. Cambridge: Heffer and Sons, Ltd., 1933. 

Although this book is now out of date and has not been revised, it is included 
on the strength of Baldwin's comment that it is "the best introductory text- 
book to the subject that has ever been written." 

BIOLOGY 

1. Alice, W. C. Cooperation Among Animals, with Human Implica- 
tions. New York: Schuman, 1951. 



448 vimtograpn? 

A nontechnical account of the simpler, more direct evidence concerning the 
beginnings of co-operation among nonhuman animals. Dr. Alice also dis- 
cusses certain implications of co-operation and their bearing on international 
relations. A book of exceptional interest and importance. 

2. Alice, W. C., Emerson, A. E., Park, O., Park, T. and Schmidt, 
K. P. Principles of Animal Ecology. Philadelphia: Saunders, 1949. 

This volume organizes and summarizes a large, complex field. Although pri- 
marily a technical monograph, many chapters are clearly and simply written 
and will appeal to the general reader. Chapter 23 on "Animal Aggregations," 
and Chapter 24 on 'The Organization of Insect Societies" bear closely on 
the discussion in Dr. Alice's essay. 

3. Bates, Marston. The Nature of Natural History. New York: 
Scribner's, 1950. 

An excellent popular survey, mainly of animal biology, addressed to mature 
readers. 

4. Beebe, William. The Book of Naturalists, An Anthology of the 
Best Natural History. New York: Alfred Knopf, 1944. 

A fine collection of essays, selected and edited by a gifted biological writer. 

5. Blum, Harold F. Times Arrow and Evolution. Princeton: Prince- 
ton University Press, 1951. (See especially Chapter 10: 'The Origin 
of Life.") 

Somewhat technical, but suitable for those with a strong curiosity about the 
subject, who are not unwilling to concentrate while reading. 

6. Buchsbaun, Ralph. Animals Without Backbones. Chicago: Uni- 
versity of Chicago Press, 2nd edition, 1948. 

Easy reading and accurate, with a wealth of superb illustrations; for intelli- 
gent persons with high school education. 

7. Carr, Archie F. High Jungles and Low. Gainesville: University of 
Florida Press, 1953. 

A rewarding book for the thoughtful, general reader. 

8. Encyclopedia Britannica, printings since 1950. 

The zoological articles have been recently carefully revised, or rewritten by 
eminent modern zoologists. This is a better source book of modern knowledge 
in the field than is generally realized. The material is usually presented in 
fairly elementary fashion. Particularly pertinent articles include: animal be- 
havior, animal sociology, biology, comparative psychology, courtship of ani- 
mals, marine biology, play in animals, social insects. The general articles on 
biology and zoology are also valuable for a quick survey and in giving leads to 
articles on other subjects. 

9. Harden, Garrett Biology, Its Human Implications. San Francisco: 
Freeman, 1949. 



Bibliography 449 

A well-written, comprehensive textbook for college freshmen. 

10. Montagu, Ashley. On Being Human. New York: Henry Schu- 
man, Inc., 1950. 

Selected bits of the scientific data supporting the idea that co-operation, not 
conflict, is the basic principle of group living are presented in this small, 
palatable book. 

11. Odum, Eugene P. Fundamentals of Ecology. Philadelphia: 
Saunders, 1953. 

A relatively simple, direct, almost popular textbook for beginners in ecology. 

12. Wheeler, William M. Social Life Among the Insects. New York: 
Ilarcourt, Brace Co., 1923. 

A brilliant description of different insect societies. Accessible to the ordinary 
reader. 

EVOLUTION AND GENETICS 

1. Darlington, C. D. The Facts of Life. London: Allen and Unwin, 
1953. 

A fascinating and unconventional account of the development of man's ideas 
on reproduction and heredity. Controversial. 

2. Darwin, Charles. The Origin of Species. London: Murray, 1859. 

3. Darwin, Charles. The Expression of the Emotions in Man and 
Animals. London: Murray, 1872. 

4. Ford, E. B. Mendelism and Evolution. London: Methuen, 1931. 
A brief but illuminating book. 

5. Goldschmidt, Richard D. Understanding Heredity. New York: 
John Wiley and Sons, Inc., 1952. 

An excellent primer by a foremost geneticist. Can be read \\ithout special 
training but requires close attention. 

6. Dobzhansky, Theodosius. Genetics and the Origin of Species. 
New York: Columbia University Press, 3rd edition, 1951. 

Perhaps the outstanding textbook in the field but on a somewhat more ad- 
vanced level than most of the other books suggested on this list. 

7. Huxley, Julian S. Evolution y the Modern Synthesis. London: 
Allen and Unwin; New York: Harpers, 1942. 

A comprehensive treatise containing numerous illustrative examples. Also a 
somewhat advanced work. 

8. Huxley, Julian S. Evolution in Action. London: Chatto and 
Windus; New York: Harpers, 1953. 



450 Bibliography 

An admirable discussion of evolution as a process and man's place in it. 

9. Scheinfeld, Amram. The New You and Heredity. Philadelphia, 
New York: }. B. Lippincott Company, 1950. 

One of the good popularisations of recent years, this comprehensive book 
offers the general reader a clearly written, fully illustrated survey of all as- 
pects of the problem of human inheritance. 

10. Simpson, George Gaylord. The Meaning of Evolution. New 
Haven: Yale University Press, 1949. 

The clearest semi-popular summary of the process of evolution and its im- 
plications for general thought. 

11. Simpson, George Gaylord. Horses. New York: Oxford University 
Press, 1951. 

An interesting account of the best known single case of the evolution of a 
group. 

12. Smith, Homer W. From Fish to Philosopher. Boston: Little, 
Brown, 1953. 

A lucid and original presentation of the course of vertebrate evolution. Pro- 
fessor Smith, an eminent physiologist and a fine writer, traces the evolution 
of man through the evolution of the kidney. 

13. Wells, H. G., Huxley, J. S. and Wells, G. P. The Science of 
Life, especially books 3, 4 and 5. New York: Doubleday; London: 
Cassells, 1934. 

A primer of the actual course of evolution; together with a summary of 
genetics, reproduction and evolution theory. Though written a quarter of a 
century ago this book remains the best all round popularization of biology. 

14. Tinbergen, N. The Study of Instinct. New York: Oxford Uni- 
versity Press, 1951. 

An engrossing study of the mechanism underlying innate behavior. In this 
and other books Tinbergen shows himself a remarkable observer of animal 
behavior, from the stickleback to the herring gull. 

15. Young, J. Z. The Life of Vertebrates. Oxford: Clarendon Press, 
1950. 

A monumental survey of all phases of vertebrate life. This is an advanced 
textbook, but it can be read by anyone with a more than superficial desire to 
enlarge his biological knowledge. 

PSYCHOLOGY 

GENERAL TREATMENTS OF PSYCHOLOGY 

1. Boring, E. G., Langfeld, H. S., and Weld, H. P., (Eds). The 
Foundations of Psychology. New York: John Wilev, 1948. 



Bibliography 451 

A thorough treatment of modern scientific psychology at a somewhat ad- 
vanced textbook level, consisting of 25 chapters written by 19 experts. Clear, 
concise, full of facts. 

2. Woodworth, R. S. Experimental Psychology. New York: Henry 
Holt, 1938. 

A clear, straightforward, simple handbook of experimental psychology, writ- 
ten in a unitary style by a single author; somewhat more technical than 
Boring, Langfeld and Weld, but not nearly so difficult as the handbooks writ- 
ten for research workers. 

HISTORY OF PSYCHOLOGY 

3. Peters, R. S. (Ed) . Brett' s History of Psychology. New York: Mac- 
millan, 1953. 

An abridgement of G. S. Brett's three classical volumes (1919 1921) on the 
history of psychology from before Socrates down into the 20th century. This 
is the standard work on pro-scientific philosophical psychology, but for the 
scientific period since 1850 it is better to consult Murphy or Boring. 

4. Murphy, Gardiner. Historical Introduction to Modern Psychology. 
New York: Harcourt, Brace, 2nd edition, 1949. 

One of the best and broadest, as well as the most readable, histories of scien- 
tific psychology, its origin and development. More inclusive than Boring, 
though less detailed in respect of the topics treated. 

5. Boring, E. G. A History of Experimental Psychology. New York: 
Applcton-Century-Crofts, 2nd edition, 1950. 

A fine exposition of the origin of experimental psychology and philoso- 
ophy and sense-physiology and its subsequent development from 1850 to the 
present. 

6. Garrctt, H. E. Great Experiments in Psychology. New York: 
Applcton-Century-Crofts, 2nd edition, 1941. 

An attractive, readable, elementary discussion of great experiments in psy- 
chology of the last 100 years: sensory measurement, sense-perception, learn- 
ing, conditioned response, brain function, reaction time, instinct, emotion, 
intelligence testing, human abilities and personality. 

SYSTEMS AND THEORIES OF PSYCHOLOGY 

7. Woodworth, R. S. Contemporary Schools of Psychology. New 
York: Ronald Press, 2nd edition, 1948. 

A small book, consisting of clear and felicitous accounts of five modern 
schools of psychology: the introspective, bchavioristic, Gestalt, psychoanalytic 
and purposivist schools. 

8. Heidbrcdcr, Edna. Seven Psychologies. New York: Appleton- 
Century-Crofts, 1933. 



452 Bibliography 

Lucid summaries of seven systems of psychology which were modern in 1933: 
William James* psychology, Titchener's structural psychology, Chicago func- 
tionalism, Columbia dynamic psychology, behaviorism, Gestalt psychology 
and psychoanalysis. Out of date but still widely used because of its excel- 
lence. 

9. Skinner, B. F. Science and Human Behavior. New York: Mac- 

tnillan, 1953. 

A brilliant modem polemic for the analysis and control of human behavior 
and conduct in respect to learning, thinking, social conduct, psychotherapy, 
government, religion, economics, education and the design of culture; the 
present culmination of a half century of behavioristic thought and effort. 



FIELDS OF PSYCHOLOGY 

10. Guilford, J. P., Ed. Fields of Psychology. New York: Van Nost- 
rand, 1940. 

Thirteen distinguished authors in 22 chapters describe the nature and con- 
tent of 12 fields of modern psychology. 



PHYSIOLOGICAL PSYCHOLOGY 

11. Morgan, C. T. and Stellar, Eliot. Physiological Psychology. New 
York: McGraw Hill, 2nd edition, 1950. 

A comprehensive text on the mechanisms of human and animal behavior, 
covering basic physiology and neurology, individual and evolutionary develop- 
ment, the senses, motor functions, learning, motivation and thought. The 
best book of its kind. 



LEARNING, MEMORY AND THINKING 

12. McGeoch, J. A. and Irion, A. L. The Psychology of Human 
Learning. New York: Longmans Green, 2nd edition, 1952. 

A compendium of the results of the experimental research on human learn- 
ing. Somewhat difficult and technical but at present the best single book 
in the field. 

13. Wertheimer, Max. Productive Thinking. New York: Harpers, 
1945. 

A brilliant little volume by the distinguished founder of the school of Gestalt 
psychology; not a systematic text covering the subject, but an analysis of 
representative cases of creative thinking, including Galileo's, Gauss's, and 
Einstein's. 



Bibliography 453 



HUMAN ABILITIES AND INDIVIDUAL DIFFERENCES 



14. Scheinfeld, Amram. Women and Men. New York: Harcourt, 
Brace, 1943. 

The simplest and also most thorough analysis of the evidence of the difference 
between the two sexes. Very easy reading. 

MOTIVATION AND PERSONALITY, NORMAL AND ABNORMAL 

15. White, R. W. The Abnormal Personality. New York: Ronald 
Press, 1948. 

An exceptionally clear discussion of the phenomena of the neuroses and 
psychoses, of dreams and hypnosis, of anxiety, defense and conflict, of 
phobias, obsessions and hysteria, and of psychosomatic disorders. 

SOCIAL PSYCHOLOGY 

16. Sargent, S. S. Social Psychology. New York: Ronald Press, 1950. 

An excellent text dealing with the relation of personality to culture, motives, 
frustration, egoism, communication, the interaction of social groups, leader- 
ship, public opinion, mass behavior, social change and movements, and 
social prejudice. 

17. Newcomb, T. M. and Hartley, E. L. (Eds). Readings in Social 
Psychology. New York: Henry Holt, 1947. 

A comprehensive work consisting of 83 excerpts from the writings of 97 
authors dealing with social and cultural effects on individual characteristics 
and on memory, judgment, perception and motivation, the development 
of socialization in the child, the effects of group situations, of social role 
and social status and of class structure, prejudice, language, suggestion, com- 
munication, propaganda, public opinion, frustration, morale, mass behavior, 
war and peace. 

PSYCHOANALYSIS 

1. Freud, Sigmund. Introductory Lectures on Psychoanalysis. Lon- 
don: Allen and Unwin, 1922. 

A systematic, yet simple and lucid presentation of Freud's main ideas and 
discoveries. Still the best primer of the subject. 

2. . New Introductory Lectures on Psychoanalysis. New York: 

W. W. Norton Co, 1933. 

The New Introductory Lectures contain Freud's later discoveries and the 
changes from the original theories as expressed in the earlier lectures. 



454 Bibliography 

3. . The Basic Writings of Sigmund Freud. New York: The 

Modern Library, 1938. 

This excellent volume contains several of Freud's classical writings. Psycho- 
pathology of Everyday Life is a readable little book which deals with the 
causes of forgetting, why we make slips of the tongue, etc. The Interpreta- 
tion of Dreams, Freud's most famous work, is fascinating, but large 
parts of it are not easy to follow. The History of the Psychoanalytic Move- 
ment is an interesting short survey of psychoanalysis and the deviations 
from it seen from the partisan position of the founder of psychoanalysis. 

4. Jung, Carl J. The Psychology of the Unconscious. New York: 
Dodd, Mead and Co., 1927. 

A detailed, fundamental presentation of his views by the foremost theoreti- 
cian who broke away from Freud. 

5. Adler, Alfred. Understanding Human Nature. New York: Green- 
berg Publishing Co., Inc., 1927. 

Another of Freud's well-known disciples (who later deviated from him) 
describes his system. 

6. Mullahy, Patrick. Oedipus Myth and Complex. New York: 
Hermitage Press, Inc., 1948. 

The theories of Freud, Jung, Adler, Rank, Homey, Fromm and Sullivan 
covered in clear, disinterested sketches. 

7. de Forest, I. The Leaven of Love. New York: Harper Brothers, 
1954. 

A well-rounded picture of the main factors in Ferenczi's therapy. 

8. Alexander, Franz. Fundamentals of Psychoanalysis. New York: 
W. W. Norton and Co., Inc., 1948. 

Freud's basic concepts and how they have evolved in application. The 
author is director of the Chicago Institute for Psychoanalysis. 

9. Horney, Karen. The Neurotic Personality of our Time. New 
York: W. W. Norton and Co., Inc., 1937. 

Horney's first work, presenting her main ideas on the essence of neurosis. 

10. . New Ways in Psychoanalysis. New York: W. W. Nor- 
ton and Company, Inc., 1939. 

The author explains how and why she departed from Freud's theories. 

11. . Our Inner Conflicts. New York: W. W. Norton and 

Company, Inc., 1945. 

A further development of Horney's theoretical thought. 

12. Sullivan, Harry Stack. Conceptions of Modern Psychiatry. 
Washington: The William Alanson White Foundation, 1947. Also, 



Bibliography 455 

The Theory of Interpersonal Relations. New York: W. W. Norton 

Co., Inc., 1951. 

Together these books offer a full statement of Sullivan's theory of inter- 
personal relations. 

13. Fromm, Erich. Escape From Freedom. New York: Farrar and 
Rinehart, Inc., 1941. 

A study of the causes of authoritarianism and an analysis of modern man's 
ways of escaping from freedom and from himself. Fromm's best-known and 
most influential book. 

14. . Man For Himself. New York: Rinehart and Co., Inc., 

1947. 

An inquiry into the psychology of ethics; an attempt to establish ethics on 
the basis of our knowledge of man's nature. 

15. . The Sane Society. New York: Rinehart and Co., Inc., 

1955. 

A study of the pathogenic effect on man of contemporary industrial society, 
and suggestions for a society more conducive to mental health. 

16. Dunbar, Flanders. Emotions and Bodily Changes. New York: 
Columbia University Press, 4th edition, 1954. 

An enormous survey of literature on psychosomatic interrelationships. Dr. 
Dunbar's book, ideal for reference and for browsing, is an encyclopedia of 
what is known today about the effect of mental behavior on our bodies. 



SCIENCE AS FORESIGHT 

1. Ashby, W. Ross. Design for a Brain. New York: John Wiley and 
Sons, Inc., 1952. 

A British psychiatrist who has performed important researches on the func- 
tioning of the brain explains the problem of designing a machine which 
will have some of the self-organizing and adaptive powers of the nervous 
system. The key, Ashby says, is the principle of "ultrastability"; and he has 
built the mechanism incorporating the principle. Half of Ashby's book is 
mathematical, half states its thesis in plain words but is difficult. 

2. Scientific American, September 1952. 

This issue of the leading U.S. science magazine has become famous for its 
comprehensive survey of automatic control. Eight contributors discuss various 
aspects of the subject: Emest Nagel, the basic ideas and their social impli- 
cations; Arnold Tustin, the theory of feedback and self-regulating processes; 
Gordon Brown and Donald Campbell, the application of feedback media- 



456 Bibliography 

nisms; Eugene Ayres, an automatic chemical plant; William Pease, an auto- 
matic machine tool; Louis Ridenour, the role of the computer; Gilbert King, 
the nature of information and communication theory; Wassily Leontief, the 
potential economic effects good and bad of automatization. The articles 
are written for the general reader and there are many excellent illustrations. 

3. Bowden, B. V. (Editor). Faster than Thought. London: Sir Isaac 
Pitman and Sons, Ltd., 1953. 

Twenty-four articles, many of general interest, on the history and theory of 
computers, on their uses in solving problems of logic, physics, astronomy, 
meteorology, ballistics, engineering, government administration, economics, 
business and commerce, and games. 

4. Shannon, Claude E. A Chess-Playing Machine. Scientific Ameri- 
can, February, 1950. 

Claude Shannon has done some of the most important fundamental work 
on the theory of communication. In this popular article he describes an 
electronic computer that can be set up to play a pretty strong game of chess. 

5. Shannon, Claude E. and Weaver, Warren. The Mathematical 
Theory of Communication. Urbana: The University of Illinois Press, 
1949. 

In this volume are presented Shannon's famous paper on the mathematical 
theory of communication, first published in 1948, and a largely expository 
and nonmathematical summary of the main concepts and results of Shan- 
non's theory by the Director of the Division of the Natural Sciences in the 
Rockefeller Foundation. A condensation of Weaver's paper couched in 
popular language appears in Scientific American, July 1949. 

6. Sluckin, W. Minds and Machines. Penguin Books, 1954. 

A clear, unpretentious, popular survey of modern automatic computing 
machines, cybernetics, information theory, and a discussion of how the study 
of these machines has influenced modern psychology. 

7. Berkeley, Edmund Callis. Giant Brains or Machines That Think. 
New York: John Wiley and Sons, Inc., 1949. 

Berkeley's readable book gives unusually detailed but rather simple explana- 
tions of the operations of different types of calculating machines including 
punch-card calculators, differential analyzers, electronic calculators, logical- 
truth calculators. So swift are the developments in this field that the latest 
machines have already gone well beyond Berkeley's book, but his introduc- 
tion retains its validity. 

8. Wiener, Norbert. Cybernetics for Control and Communication 
in the Animal and the Machine. New York: John Wiley and Sons, 
Inc., 1948. 

A landmark in its field. While much of the discussion is technical and quite 
advanced there are sections which will fascinate almost any reader. Wiener's 
popular book (The Human Use of Human Beings, Houghton, Mifflin, New 



Bibliography 457 

York, 1950) is a rambling essay giving the author's views on almost any 
subject that popped into his head, but a few chapters are lively and 
enjoyable. 

9. Walter, W. Grey. The Living Brain. New York: W. W. Norton 
and Company, Inc., 1953. 

An account of the researches of the last twenty years on the mechanics of 
the brain. Overwritten, but an absorbing book. 

10. Turing, A. M. Computing Machinery and Intelligence. Mind, 
October, 1950. 

A brilliant essay which considers the question "Can a machine think?" Clear, 
original and profoundly interesting. 

11. Jeffress, Lloyd A. (Editor). Cerebral Mechanisms in Behavior 
(The Hixon Symposium). New York: John Wiley and Sons, Inc., 
1951. 

This volume consists of six papers by different specialists concerned with 
the problem of the brain as a machine. The outstanding essay, by John 
von Neumann, on the general and logical theory of automata, considers the 
question whether it is possible to design and construct a machine capable 
of reproducing machines of its own kind. Von Neumann argues that it is 
possible. 



Index 



A-bombs, manufacture, 15 

abnormal, definition, 344 

absolute threshold, 301 

acctaldehyde, 182 

acetic acid, 182 

acetyl-coenzyme, 212-213, 222 

acetylene (ethyne), 181 

Ach, N. f 310 

Achilles, race with tortoise, 29, 31 

acids: 

halogens, 170 

hydrolysis, 215 

ionic compounds, 177 
acquired characters, inheritance, 257, 

258, 274 

activities, constant and variable, 241 
activity, physiological need, 311 
adaptation and logic, 413-414 
adaptive machines, 405-414 

adaptation and logic, 413 

experience in machines, 407 

exploring machine, 412 

goal-seeking strategy, 405 

unlimited foresight, 406 
addition reaction, 181 
adenosinediphosphate (ADP), 215-217 

formation, di'ag., 216 
adenosinetriphosphate (ATP), 215-217 
Adler, Alfred (1870-1937), 377, 378 
administration problems, dependent 

peoples, 354 

adopted infant, adaptability, 331 
ADP, see adenosinediphosphate 
Adrian, Sir Edgar Douglas (1889- ), 

quoted, 14 
adrenalin, 210, 222 
Africa, South, ape-men, 322, 323, 324, 

330 
Africa, tropical, toolmaking, 322 



African culture, plough and wheel, 385 

afterlife, denial, 344 

age, galaxies, 95 

age regression, 367 

aggregation of matter, three states, 156 

aggressiveness, animal, 243-244 

agriculture. 

dependence on chemistry, 178 

soil exhaustion, 7, 8 
air: 

chemical nature, 165 

combustion, 162, 163 

embodiment of qualities, diag., 156 

movement, tropical forest, 239 
airplane night flier, visual sensitivity, 

303 

d-keto acids, 208, 209 
d-ketoglutaric acid, 209 
alanine, 208; formula, 207 
Alaska, artifacts, 326 
albinism, 261 
albumin, egg, 205 
alchemical emblem, illus., 161 
alchemists, puffers, illus., 158 
alchemy: 

chemistry, 158 

end of, 162 

origin and tenets, 157 

traditional, 274 

alcohol, 181-182; intoxication, 368 
aldehyde group, organic chemistry, 182 
Alexander, Franz, 378 
algae, 235 

algebra, Boolean, 49-50 
algebraic geometry, 394 
alkali metals, 170 
alkaloids, 188 
Alice, Warder Clyde (1885-1955), 228- 

230 

alleles, 267-268 
alloys, ancient knowledge of, 155 

459 



460 



Index 



alpha particles: 

deflection, 125-126 

ejection from radium, 129 

polonium, interaction with, 130, 131, 
diag., 130 

summarized, 147-148 

transmutation, 174 

uranium, interaction with, 130, 131, 

diag., 130 

alum, ancient knowledge, 155 
aluminum, symbol, 169 
American Indian: 

cultures, 330 

language similarities, 350 
amino acids: 

deamination, 222 

essential, 206, 218 

formulae, 207 

glucogenic, 212 

ketogenic, 212 

metabolism, 212 

new tissue formation, 205 

proteins, 204, 205, 206, 207, 208, 
232 

surplus, 208, 209 

tyrosine, 222 
ammonia: 

basis for life, 237 

components, 168 

derivatives, 182-183 

discovery, 164 

earth, early atmosphere, 232 

excretion, 209 

molecule, 174 

symbols, 168 

toxicity, 209 

ammonites, fossil evidence, 280 
amphibians: 

partial colonization, 281 

territorial defense, 243 
amylase, 203 
anabolic process, 200 
anaerobic bacteria, 236 
analogue machines, 389; diag., 390 
analysis into units, 428 
anatomy, studies, 256 
Anaximander (611?-?547 B.C.), 25 
Andean culture, 328 
Anderson, Carl David (1905- ), 

104, 143, 146, 148 
andromeda nebula, 81 
Angel, J. L., 337 



angle, tetrahedral, 192 

aniline, 183, 185 

animal behavior, Harvard law of, 238 

animal breeds, outward appearance, 332 

Animal Ecology, Principles of, 237 

animals: 

adaptation to environment, 385 

animal-plant relation, 236 

behavior patterns, 233, 240, 405 

biochemistry, 199 

carnivorous, 218 

change in unfavorable surroundings, 
245 

communal reaction, 243 

community living, 247 

continuous transformation, 274 

diet experiments, 219-220 

domestication, 325, 326 

evolution, 246, 273 

experimental psychology, 308 r 310 

fossil, 277 

genetic mechanism, 267 

group survival, 245-247 

herbivorous, 218 

induction, 433 

light, reactions to, 237 

mutation, 265 

nutritional requirements, 219, 220 

population regulation, 288 

protein diet, 208 

proto-co-operation, 247 

separate species, 279 

social rank responsibilities, 244 

sociality, 233 

stabilization, 282, 284 

synthetically deficient, 218 

telegony, 259-260 

tropical rain-forest, 239 
anthracine, formulae, 184 
anthropological Monroe Doctrine, 326, 

327 

anthropological publication, 356 
anthropologist, primary role, 354 
anthropology, 319-357 

constitutional, 335, 353 

cultural, 319, 338, 340, 354, 356 

historical, 352 

human biology, comparative, 330-337 

human evolution, 321-322 

industrial, 354 

linguistics, 345-352 

man, history of, 322-329 



Index 461 



anthropology (cont.) 

physical, 353 

psychoanalysis, 378, 379 

range of enquiry, 319-320 

techniques, 340 

uses, 352-357 

ways of men, 338-345 
anti-proton, mass particle, 149 
anti-vitamins, 224 
antibiotics, 188, 222-224 
antigen, Henshaw, 333 
ants: 

fixed behavior, 405 

stabilization, 282 

tropical rain-forest, 239 
anxiety, role of, 378 
ape, introspection, 300 
ape-men (Australopithecines), 322, 323, 

324, 330 
aptitude, 312 
Aquinas, Saint Thomas (12257-1274), 

61 
archaeology, 319; role in public adult 

education, 352 

Archimedes (2877-212 B.C.), 15, 37, 44 
Arctic area, early population, 326 
Aristotle (384-322 B.C.): 

four elements, 155, 159, 161, 162 

logic, 52, 61 

matter, unity, 173 
arithmetic, a new, 394-399 
arithmetic continuum, 44 
arithmetical machines, 389-391 
arithmetical puzzles, 45 
Arizona, cave cultures, 328 
aromatic compounds, 183 
art: 

function, 248 

libidinal forces, 372 

Paleolithic Age, 325 
arthritic conditions, cortisone, 223 
artifacts: 

Alaska, 326 

circumpolar region, 326 

dating, 328 
artificial elements, 172 
artistic creation, neurotic symptom, 377 
artists and writers, great, cycles, 339 
ascorbic acid (vitamin C), 218, 219 
Ashby, Dr. Ross, 412, 413 
association: 

axioms of, 36 



association: (cont.) 

free, 368-369 

laws of, 307 

assumptions, cosmology, 85-94 
astrolabe, 386 

astronomical space geometry, 31-33 
astronomy, 66-96 

calculation, 58 

cosmology, 84-96 

galaxies, 81-84 

physical principles, 103 

reaction time, 305-306 

solar system, 66-69 

stars, 69-81 

tools, 386 

asymmetric forms, 191, 192, 193 
atmosphere, earth, 76 
atomic: 

bomb, 140, 174 

energy, constructive application, 174, 
288 

mechanics, 129 

nuclei, 105, 135, 140 

numbers, 135 

physics, 79, 415; particles summa- 
rized, 145-149 

power, replacing oil, 8 

power stations, 10 

reactions, code, 431 

structure, 103; diag., 171 

theory, 102, 166, 167, 170 

weight, atoms, 168 
Atomic Energy, U.S. Senate Special 

Committee on, 99 

atomistic school, solid geometry, 29-30 
atoms: 

arrangement, 144 

atomic weight, 168 

behavior, 104, 105 

chemical nature, 135, 172 

crystals, 124, 125 

Daltonian symbols, illus., 168 

deflection, 125-126 

distance between, 391 

electronic constitution, 170 

ion, 137 fn., 171 

light-emitting properties, 103, 127, 
134 

molecules, 174 

motion of electrons, 127 

Newton's theory, 167 

nuclear, 126 



462 Index 



atoms: (cont.) 

ratio of forces, 92 

self-linking, 180 

sodium, diag., 172 

splitting, 170 

structures, diag., 171 

valency, 175 

ATP, see adenosinetriphosphate 
attention degree, measuring, 306 
attitude and need, concepts, 311 
aureomycin, 223 
Australia, fertility, 10 
automatic pilot, 409, 412, 413, 422 
automatic scanner, 386 
automatic timer, 386 
automatic voting machine, 387 
Avogadro's hypothesis, 175, 177 
axes, hand, 324 fn. 
axioms: 

Euclid, 36 

Greek, 25-26 

mathematics, 39 

new views, 36-37 
azo dyes, 189 
Aztec civilization, 328 



B 



Babbage, Charles (1792-1871), 400, 

435 
Babylonians: 

algebra and geometry, contributions 
to, 27 fn. 

hypotenuse, length, 26 

numerical problems, solving, 24, 45 

surveying and measuring, 25 
background noise, 421 
Bacon, Francis (1561-1626), 62 
bacteria : 

anaerobic, 236 

experiments, 220 

genes, 267 

metabolism, 224 

nutritional requirements, 219, 220- 
221 

self -reproduction, 261 

toxins, 221 

vitamins, 220, 221 
bacteriostatics, 222-224 
Baldwin, Ernest (1909- ), 196-197 
Bally, Gustav, 378 
barbarism, reversion to, 13 



barrier leakage, natural radioactivity, 

134 

bases, ionic compounds, 177 
Basques, blood group gene, 333 
Bateman, Harry, 20-21 
Bateson, William (1861-1926), 264 
beams, energy, 74 
bees, spontaneously generated, 257 
beetle, burying, 405 
behavior: 

instinctive, 240-241 

linguistic, 350 

patterns, 233, 240-242, 338 

physique-behavior relation, 335 
behaviorism, 299, 300, 301, 308 
beliefs, needed changes in, 16 
benzene ring, 183, 185, 430; diag., 184 
Bergson, Henri (1859-1941), 272 
Bernoulli, James, 58 
beryllium : 

symbol, 169 

transmutation, 174 

Berzelius, Jons Jakob (1779-1848), 168 
Bessel, Friedrich Wilhelm (1784-1846), 

305 

beta-emitters, 141-142 
beta-processes, 147 
beta -rays, 125 

Bethe, Hans (1906- ), 140 
binary notation, diag., 304 
binary scale, 48 
binary stars, motion, 69 
biochemical quantum, 215 
biochemistry, 198-225 

carbohydrate metabolism, 210-213 

carbohydrate storage, 204-205 

citric-acid cycle, 213-214 

digestion, 203-204 

energy metabolism, 214-218 

enzymes, 201-203 

fat metabolism, 210-213 

fat storage, 204-205 

hormones, antibiotics, bacteriostatics, 
222-224 

metabolism, 199-200 

organic chemistry, 178 

organic molecules, 193 

pharmacology, 222 

protein foods, 205-210 

therapeutics, 222 

vitamins, 218-222 
biogeography, 233 



Index 463 



biological: 

adaptation, 279 

constitution, effect on personality, 
342 

evolution, 272, 277-280, 286 

genetics, 285 

organization, stabilization, 282 

panorama, 284 

problems, chemical methods, 198 

sciences, 154, 250 

substances, isolation, 223 

work, 200 
biology, 231-252 

biology-religion relation, 233-234 

classification problems, 233 

divisions, 232 

organic chemistry, 178 

physical knowledge, 103 
birds: 

crocodile, 385 

dominance on land, 281 

peck orders, 244 

stabilization, 282 

territorial defense, 243 
birth difficulties, human, 331 
birth trauma, 377 
Black, Joseph (1728-1799), 163 
Blake, William (1757-1827), quoted, 

160 

blood, glucose concentration, 210, 211 
blood cells, sickling, 333 
blood groups, variations, 333 
blood poisoning, bacteria, 220-221 
blue sky, 421 
blue stars, 71, 81 

bodies, large, mechanical motions, 102 
bodily structure, evolution, 272 
Bohr, Niels (1885- ), 103, 126, 

127, 128, 133, 171 
Bondi, Hermann (1919- ), 64-65 
Boole, George (1815-1864), 49, 50, 52 
Boring, Edwin G. (1886- ), 292- 

293 

Born, Max (1882- ),98, 103, 132 
boron, symbol, 169 
bottled gas, 180 

Bouguer, Pierre (1698-1758), 295 
Boyd, W. C., 333 
Boyle, Robert (1627-1691), 159, 162, 

164 
brain : 

electronic, 404 



brain: (cont.) 

expansion, 321, 323-324, 389 
human, visual portions, 303 
mind, interaction with, 298 
organ of psychological studies, 308- 

309 

breathing mechanism, insects, 283 
Breit, Gregory, 138 
Bridgman, Percy Williams (1882- ) , 

300 

bright stars, 72, 80, 84 
Broglie, Prince Louis de (1892- ), 

103, 127, 128-129 
Bronowski, Jacob (1908- ), 382- 

384 

Brouwer, L. E. f., 55 
Bullard, Dexter (psychoanalyst), 374 
burying beetle, 405 
business and industry, anthropological 

techniques, 340 
butane, formulae, 180 
Butler, Samuel (1835-1902), 271 
butterfly, protective coloring, 276 



calcium, dietary, absorption, 221 
calcium carbide, 182 
calcium compounds, dimmed stars, 83 
calculating machine, 389, 391 

logical machines, 435 

program tape, diag., 402 

step-by-step approximation, 394; 

diag., 402-403 
calculation, reach of, 414 
calorie requirements, calculations, 217 
calx (oxide), 163, 166 
camera, 386 

cancer therapy, uranium reactors, 144 
candle-meters, 238 
carbohydrates: 

function, 186 

katabolism, 201 

metabolism, 205, 209, 210-213 

oxidation, 214 

storage, 204-205 

tissue requirements, 210 
carbon : 

basis for life, 237 

compounds, chemistry of, 179 

dimmed stars, 83 

food cycle, dwg., 187 



464 Index 



carbon: (cent.) 
symbols, 168, 169 
transmutation, 174 
carbon atoms, 211, 212, 213, 214, 217 

asymmetric, 192 

linking, 179, 180, 183; diag., 184 
valencies, 179, 191; diag., 192 
carbon dioxide, 163, 164 

formulae, diag., 176 

symbols, 168 

Carbon 14 technique, 329 
carbon monoxide, 182 
carbonic oxide, symbols, 168 
carboxyl group, 182 
cardinal numbers, 41, 42 
carnivorous animals, 218 
cash register, 391 
catalyst: 

chemical reaction, 181 

enzymes, 201-203 

neutrons, 160 

philosopher's stone, 1 59 
cattle, hornlessness, 261 
causality, principle, 60 
caustic soda, 170 
cave cultures, 328 
Cavendish, Henry (1731-1810), 165, 

166 
cells: 

chromosomes and genes, 267 

divisions, 260 

gametes, 260 
cells, living: 

chemical changes, 200, 202 

composition, 199 
cellulose, macromolecules, 190 
censors, objection to useful knowledge, 

12 

census taker, 387 
Chadwick, Sir James (1891- ), 103, 

135, 147 

chalk, heated, 163, 164 
chance, games based on, 415 
character: 

changes, 11 

differences, 261-264 

Mendelian factors, 264 

neurotic, 373-374 

character traits, organic inferiorities, 377 
Chaucer, Geoffrey (1340-1400), 

quoted, 155 
checkers, game, 406 
chemical action, linking atoms. 430 



chemical bonds, concept, 431 
chemical elements, formation, 272 
chemical energy, scale, 391 
chemical equation, 177 
chemicals, synthetic, 223 
chemistry, 154-194 

alchemy, 157-162 

atomic theory, 166-178 

combustion, 162-166 

inorganic and organic, 178-194 

self -reproducing matter, 266 

space, 193 

use of modem physics, 103 
chess-playing machine, 406, 409-410 
chicken, high-ranking males, 244 
child-relationships, 379 
Child Training and Personality (Whit- 
ing and Child), 343 
child training system, effect on person- 
ality, 342 
childhood: 

experience significance, 378 

importance of first years, 369 
chimpanzees, cranial capacity, 324 
China: 

contacts with New World, 327 

epistemology, 351 
Chippewa Indians, aboriginal culture 

influence, 342 
Chittenden, Russell H. (1856-1943), 

206, 208 

chlorides, saliva, 202 
chlorine : 

discovery, 165 

symbol, 169 
chloromycetin, 223 
chlorophyll green: 

development, 232 

plant pigment, 186 
chloroprene, molecules, 190 
chromophores, 189 
chromosomes: 

cell organs, 260 

doubling, 276 

mutations, 265 

number of kinds, 267-268 

organs of heredity, 261 

self -reproducing system, 261 

sex, 260 fn. 

diags., 262, 263 
chronoscopes, 305 

Churchill, Sir Winston (1874- ), 
auoted. 174 



Index 465 



chymotrypsin, enzyme, 204 
circuit as a counter, diag., 392 
citric-acid cycle, 213-214, 222; diag., 

213 

citrus fruits, vitamin C, 219 
civil defense, thermonuclear weapons, 

13 
civilization: 

classical, 326 

modern, 248 

rise and fall, 337 
Clark, Colin, 399, 400 
Clark, John, 435 
Clifford, William Kingdon (1845- 

1879), quoted, 32 
climate, tropical rain-forest, 238-239 
clinics, psychoanalytic institutes, 375 
clock, 387 

basis of modern life, 386 

digital machine, 389 
clothes, fashion changes, 339 
clouds: 

dust, 83, 88 in. 

gas, 83-84 

radioactive, 13 

"Coal Sack/' Milky Way, 83 
coal-tar: 

chemistry, 184 

dyes, 189 

primaries, formulae, 184 
cocaine, natural, 189 
Cockroft, Sir John, 103, 134, 136, 139 
code: 

breaking, 436 

linguistic analysis, 352-353 

organization in, 426 

redundancy, 423 
code of nature, breaking, 429 
coin tossing, 60 

strategies, 416-417 
colchicine, 276 

cold, extreme, body responses, 335 
cold gas, 83 

collision, producing, 77-78 
collision mechanics, laws of, 125 
color-luminosity, stars, diag., 71 
Columbia University, psychoanalytic 

training, 376 
Columbia, Christopher (14467-1506), 

15, 326, 327 

Coma Berenices, nebula, illus., 82 
combustion: 

fat and carbohydrate, 210 



combustion: (cont.) 

nature of, 161, 162 

theory, 166 
common air, 163, 165 
common notions, principles of logic, 26 
communication: 

and information, theory, 388 

true speech, 284 fn. 
communication needs, speakers and 

hearers, 349 

communities, Mesolithic Age, 325 
community, linguistic, 346 fn. 
community living, animal, 247 
competitiveness-aggressiveness, 372-373 
Complex Variable, Theory of Functions 

of a, 47 
complexions, tanning by sunlight, 257, 

258 

compound atoms, 167 
compounds, molecules, 174 
Compton, Arthur H. (1892- ), 124, 

125, 133 

conditioned response, 307 
Condon, Edward U. (1902- ), 98- 
101 

wave theory for nuclear particles, 129 
conflicts, unconscious, 374 
congruence, axioms of, 36 
conscious co-operation, animal, 243 
consciousness, incorporeal events, 295 
constant composition, atomic theory, 

167 

constants, physical, 92 
constitutional anthropology, 335, 353 
contents of the unconscious, 375 
contiguity, frequency of, 307 
control mechanisms, 387 
convenient memory, 312 
Cook, Captain James (1728-1779), 218 
Coon, Carleton, 317 
co-operation: 

beginning of, 233, 235 

natural, 244-245, 246, 247-248 
Copernicus, Nicolaus (1473-1543), 
362, 364 

model, 67, 68 
copper, symbol, 169 
corpses, disposal, 344 
corpuscular theory of light, 115-117, 

121-122; dmg., 116 
correlation, theory of statistics, 59 
cortisone, 223 
cosmic rays, 143 



466 



Index 



cosmological phase, 279 
cosmology, 84-96 

comprehensive theory, 90-96 

evolutionary approach, 278 

subject matter, 84-90 

see also astronomy 
cosmos, early views, 155 
Coulomb, Charles A. (1736-1806), 

130 

Coulomb barrier, diag., 130 
counters, scale, 391 
Cours de Chymie (LeVnery), 160 
covalency: 

directional, 191 

nonpolar bond, 176 
cows, hook orders, 244 
cradle of mankind, 326 
cranial capacities, 324 
creation, myth of, 271 
creation of matter, continual, 93 
creative insight, unconscious, 298, 299 
creative thinking, 297 
crime detection, time reactions, 306 
crocodile bird, 385 
cross-staff, 386 
cryptography, 432 
crystals: 

atoms, 124, 125 

structure, 430 
cubic equation, 46 
cultural anthropology, 319, 338, 340, 

354, 356 
cultural development, organisms and 

stages, table, 323 
cultural diffusion, 286 
cultural divergence in man, 287 
cultural evolution, acceleration, 285 
cultural innovations, spread, 338-339 
cultural realm, nature of proof, 357 
cultural relativity, 343 
cultural variation, 345 
culture: 

growth, repetitive patterns, 337 

history, vocabulary analysis, 346 fn. 

influence on personality, 342 

medieval, 362 

sublimation, effect, 371 

technical term, 338 
Culture, The Nature of (Kroeber), 339 

fn. 

cultures, high, mongrel, 337 
cultures, Neolithic, spread, 326 
cultures, similarity, 344 



cumulative transmission of experience, 

284 

cure, psychoanalysts' method, 374 
Curie- Joliot, Fre"denc (1900- ), 103 
cybernetics, 9 

cycles, culture growth and change, 339 
cyclic molecular structures, 185 
cyclotron, 139 
cytology, 232 
cytoplasmic inheritance, 261 



D 



Dalton, John (1766-1844), 166, 167, 

168, 170, 430 

Daltonian symbols, illus., 168 
Darlington, C. D., 257 fn., 276 
Darwin, Charles R. (1809-1882), 244, 
246, 247, 259 fn., 269, 271, 272, 
274, 363; quoted, 436 
dating: 

anthropological, 328 

linguistic, 329-330 

tree-ring, 329 

Davis, Bergen, quoted, 132 
Davisson, Clinton Joseph (1881- ), 

128 
death: 

ceremonializing, 344 

drive for, 371 

decimal system numeration, 47-48 
decision by calculation, 415 
decoding, scientific theories, diag., 431- 

432 

deduction, logic of, 404, 433 
deductions, mathematics, 39 
deductive machines, 388-404, 406 

analogue, 389; didg , 390 

arithmetical, 389-391 

logic of the machines, 400-404 

new arithmetic, 394-399 

New Political Arithmetick, 399-400 

speed, problem of, 391-394 
deficiency disease, 218 
definitions, mathematics, 39 
de Me>6, Chevalier, 415 
Democritus, 29, 166 
Dempster, A. J., 136 
density, stellar matter, 76 
dentistry, physical anthropology contri- 
butions, 353 

dependent peoples, administration prob- 
lems, 354 



Index 



467 



dephlogisticated air, 165, 166 
dermatology, physical anthropology con- 
tributions, 353 

Desargues, Gerard (1593-1662), 37 
Descartes, Ren6 (1596-1650), 106 fn., 

155, 298 

deserts, environment for life, 237 
desires, reasons for, 364 
destinies, association with planets and 

metals, 155 

destructiveness, role of, 371 
determining tendency, 310 
deuterium, discovery, 135 
deuterium oxide, 173 
dcutcron, summarized, 147 
de Valera, Eamon (1882- ), 21 
Devonian vertebrates, 281 
de Vries, Hugo (1848-1935), 273 
diabetes: 

diagnosis, 198 

insulin, 223 

metabolism, 210-212 
diagnosis, chemical tests, 198 
diagrams, geometrical proofs, 36 
diet, influence on disease, 219 
differential threshold, 301 
diffraction: 

atom arrangement, 144 

light, 117; illus., 118 

X rays, 124 

diffusion, ideas and techniques, 339 
digestion, enzymes, 202, 203-204 
digital machines, 389 
dimmed star, 83 
dinosaurs: 

extinction, 6, 16 

fossil evidence, 280 
diploid chromosomes, 260 
Dirac, Paul A. M. (1902- ), 98, 

132, 146 
"Directions for knowing all dark 

things," 45 

disease, diet influence, 219 
dissociation, states of, 366-367 
distance, observable, 90 
distant regions, Giber's assumptions, 85 
divergent specialization, 280, 281 
Dobzhansky, Theodore, 278 
dog: 

cerebrum removal, 309 

conditioned response, 307 

emergency emotion, 309 

fight orders, 244 



dominance hierarchies, 243 
dominance orders, humans, 244 
dominant groups, 281 
dominant types, successions of, 282 
Doppler, Christian Johann (1803- 

1853), 432 
Doppler shift, 70 fn. 
draughts, game, 406 
dreams, wish fulfillment, 366 
Drosophile (fruitfly), mutation, 265 
drugs, expression of unconscious feel- 
ings, 368 

Dunn, L. C., 262 fn., 263 fn. 
Dust Bowl, 16 
dust clouds, 83, 88 fn. 
dust shot, animal collecting, 239 
dwellings, Paleolithic Age, 324 
dyes: 

artificial, 189 

natural organic compounds, 188 
dynamic psychology, 297 
dynamo, 386 



ear, sensitivity, 302, 303, 304 
earth: 

atmosphere, 76, 232 

embodiment of qualities, diag. y 156 

environment for living organism, 237 

motion through ether, 110 
Eastern Hemisphere, cradle of mankind, 

326 
Ebbinghaus, Hermann (1850-1909), 

296, 307 

eclipse, moon and sun, 69 
ecology, 232, 236, 256 
economic freedom, limitation, 10 
economic life, Mcsolithic Age, 325 
economics, problems, 399 
economy, food-producing, 325-326 
Eddington, Sir Arthur Stanley (1882* 

1944), 21, 33 

Edison, Thomas A. (1847-1931), 386 
education : 

role of archaeology, 352 

world needs, 16 
egg timer, 391 
egg white, molecules, 205 
ego and id, conflict between, 373 
ego development, 378 
Egyptians: 

four-elements theory, 155 



468 



Index 



Egyptians: (cont.) 

geometrical facts, 25 

numerical problems, 24, 45 

Ouroboros serpent, 183; illus., 184 

pyramid-builders, 26 

surveying and measuring, 25 
Ehrlich, Paul (1854-1915), 223 
Einstein, Albert (1879-1955): 

electrons, liberated, 123 

gravitation theory, 33 

light velocity, 110 

mass-energy relation, 136, 138, 145 

motion, equations, 114-115 

quantum, 145 

relativity, theory of, 103, 108, 113, 
127, 274, 362 

space and time measurements, 111, 
112 

wave-particle duality, 132 
Eisenhower, Dwight D. (1890- ), 

100, 393 

elastic solids, 106, 107, 108 
election forecasts, UNI VAC, 393, 400 
electoral seats, machine counting, 393- 

394 
electric: 

conduction, 389 

current, topology, 35-36 

discharge, 215, 232 

forces, atom, 92 

motor, 387 

electrical analogue, diag., 390 
electrical particles, behavior, 104 
electricity : 

positive or negative, 142 fn. 

power generated by uranium fission, 

140 

electrolytic dissociation, 177 
electromagnetism : 

laws, 108, 113 

logical theory, 106-107 

mathematics, 111 
electromagnets, 305 
electron : 

atomic nucleus, 105 

behavior, 104 

code, 431 

crystal atoms, 124 

diffraction, 144 

discovery, 430 

ejection, 123 

energy in X-ray tube, 115 

helium, 127 



electron: (cont.) 

localizing, 133 

motion in atoms, 127 

nuclear atom, 126 

positron, 142 

speed, 79 

spin, 106, 127 

summarized, 145-146 

unit of negative electricity, 170 

valency, 171, 172, 175, 176, 177 
electronic brain, 387, 404 
electronic machine: 

arithmetic, 393 

chess problems, 406 

problem of speed, 391-393 
electrovalency : 

nondirectional, 191 

polar bond, 176 
elements: 

artificial, 172 

material embodiment of qualities, 
diags., 156, 194 

modem table, 172 

molecules, 174 

periodic table, 169 

symbols and atomic weights, 136, 
168, 169 

transmutation, 103, 135, 156 
elephants, fossil evidence, 280 
"Elephants and Ethnologists," 327 
elixir of life (elixir vitae), 158 
Elliot-Smith, Grafton, 327 
elliptic geometry, 34 
embryology, 256, 272, 273 
emergency theory of emotion, 309 
Emerson, A. E., 230 
emotional responses, eliciting, 367 
emotions, mass, 12 
Encyclopaedia Britannica, 233 
endothermic chemical changes, 178 
energy : 

alpha particle, 129, 131 

biological work, 200 

body requirements, 210 

cycle, diag., 215 

electron, 123 

expenditure, 217 

helium, 139 

inertia, 114 

kev, 142 

light beam, 122 

metabolism, 214-218 

organic, 188 



Index 469 



energy: (cont.) 

phosphate radicle, 216 

production, 78 

psychic, transforming, 380 

quantum, 145 

scale, 391 

solar, 140 

stellar, 77 

uranium atom split, 139 

X-ray quantum, 123 
energy-mass relation, 136, 138, 145 
energy-yielding processes, 201 
entomology, 232 

entrophy and information, 424-426 
environment: 

acquired characters, 257 

adjustment to, 235, 236, 378 

biochemical adaptation, 210 

changes, 6-7, 16, 276 

exploring machine, 412 

fitness, 237 

genes mutation, 259 

influences, 334 

or heredity, 259 

uniform, 259 
enzymes: 

biological catalyst, 201-203 

classes, 202 

coenzymes, 202 

competitive inhibition, 224 

digestive, 203 

formation, 200 

gas gangrene organisms, 221 

heat susceptibility, 202 

muscle, 215 

oxidizing, 222 

peptidases, 204 

separation, 203 

specificity, 202 

transaminases, 222 

transferring, 203 

zymase, 181 

Epicurus (3427-270 B.C.), 166 
equals added to equals, 26 
equation, chemical, 177 
Equidae, horse family, 280 
equilibrium, nitrogenous, 206, 207, 208 
erg, energy, 302 
Eskimo culture, 328 
Eskimos, Alaskan, contacts with China 

and Korea, 327 
estrogens, synthetic, 223 
ethane, formulae, 180 



ether: 

all-pervasive, 106 fn., 107, 108 

luminiferous, 115 

ethics, private, affected by science, 16 
ethyl alcohol: 

equations, 181 

production, 182 
ethylamine, 183 
ethylene: 

molecules, 189 

reactivity, 181 

symbols, 168 
Euclid (fl. 300 B.C.): 

axioms, 36 

geometry definitions, 38 

parallel axiom, 30, 31 
Euclid, Elements of, 27, 39, 61 
Europe: 

Mesolithic Age, 325 

Neanderthaloid races, 323 

Neolithic Age, 325-326 

Paleolithic Age, 323-324 
evaporation rate, tropical forest, 239 
evolution, 271-289 

animals, 246 

artificially directed, 276 

biological, 272, 277-280, 286 

change, 269, 271, 273, 275 

Darwin's theory, 244, 363 

defined, 278 

human, 321-322 

natural selection, 246-247 

progress, 283 

studies, 256 

transformation, 274 

universal process, 272 

virus, 234 

see also genetics 
Evolution (journal), 278 
exact calculation, distrust of, 394 
exceptional individual, importance, 287 
exclusion principle, atomic physics, 79 
excretory products, deamination and 

formation, diag., 209 
existence, struggle for, 244, 251 
existence-theorems, mathematics, 39 
exothermic reactions, equation, 177 
exotic languages, study, 353 
expanding-universe theory, 33 
experience: 

cumulative transmission, 284, 285 

fossilization, 406 

in machines, 407-412 



470 Index 



experience: (cont.) 

interpreting, 350 

experimental psychology, 295, 296, 298, 
301, 308, 310 

Germany, 299 
experimental sciences, 433 
experiments: 

physics, new, 104-105 

use of, 432 

exploring machine, 412-413 
explosives, organic, 188 
eyes: 

insects, 283 in. 

sensitivity, 301-302, 303, 304 



factitious airs, 165 

factorial analysis, 313 

factors, interaction between, 264 

faint stars, 71, 72, 80, 85 

falcon, eyes, 279, 283 

family, differences in, 268-269 

fat men, professional, 204 

fathers, effect on nature of offspring, 

261 
fats: 

carbohydrate, 204, 213 
katabolism, 201, 211 
metabolism, 210-213 
oxidation, 214 
storage, 204-205 
Fechnei, Gustav Theodor (1801-1887), 

294, 295, 298, 301, 314 
Ferenczi, Sandor, 377 
Fermat, Pierre de (1601-1665), 560 
fermented liquors, ancient knowledge, 

155 

Fermi, Enrico (1901-1954), 103, 147 
fertilizers: 

enemy corpses, 8 
food production, 7 
fight orders, dogs, lizards, mice, 244 
figures, similarity, 26 
file, cutting teeth, 387 
finger game, strategy, 417; diag., 418 
Finlay-Freundlich, E., 33 
fire: 

discovery, 386 

embodiment of qualities, diag., 156 
sulphur-mercury theory, 158 
fireflies, light, 214 
Fisher, R. A., 266, 274, 275 



fishes: 

electric organs, 214 
intercrossing, 270 
nip orders, 244 
territorial defense, 243 
fission, 139-140, 391 
Fitzgerald, George Francis, 21, 111; 

quoted, 33 

fixed air (carbon dioxide), 163 
fixed proportions, law of, 167 
fixed stars, 66 
flakes, flint, 324 
Fleming, Sir Alexander (1881-1955), 

223 
flies: 

genes, number, 267 
spontaneously generated, 257 
flint flakes, 324 
flower-color, differences, 261 
fluorine, symbol, 169 
fog, better vision in, 421 
food: 

absorption, 204 
cycles, diag. 187 
energy yields, 217 
molecules, 203, 214 
production, 7 
protein, function, 205-210 
raising, planned, 325 
vital need, 31 1 

forces, electromagnetic, 103, 107 
forces behind observal phenomena, 362- 

363 

forecasting machine, 387 
foreign tongue, reproducing sounds, 347 
foresight: 

and insight, 427 
strategy, 388 
unlimited, 406 407 
forest, climate changes, 239 
formation, process, 75 
formula, molecular, 175 
Forsyth, Andrew Russell (1858-1942), 

21 

fossilization of experience, 406 
fossils: 

animal groups, 277 
biological evolution, 280 
hominids, 273 
human, dating, 328 
primate, 322 

four-dimensional manifold, 40 
fowls, comb changes, 264 



Index 471 



Frankland, Edward (1825-1899), 175 

Franklin, Benjamin (1706-1790), 385 

free association, 368-369 

free assortment, genetic law, 268 

freedom, limiting, 10 

freedom of choice, illusion, 364 

French Revolution, new explosives, 15 

frequency of contiguity, 307 

Freud, Sigmund (1856-1939), 297, 

298, 299, 310, 363, 364, 372 
Fricker, Peter Racine, 384 
frogs, spontaneously generated, 257 
Fromm, Erich (1900- ), 360-361, 

378 

Fromm-Reichmann, Frieda, 374 
fundamental qualities, elements em- 
bodiment of, diag., 156 
furan ring, diag., 186 
future, anticipation of, 427 



galaxies: 

aging, 95 

arrangement, 66 

condensation, 94 

evolutionary process, 278 

observable properties, 96 

recession, 86,90, 91 

spiral, 81, 83; illus., 82 

stars, 66, 81, 85,95 

systematic motions, 89 

uniformity in distribution, 89 
Galileo (1564-1642), 15, 62, 67, 102, 

415, 430 
gall wasp, 405 

game-playing machines, 406-407, 409 
games : 

based on chance, 415-420 

models for purposeful activities, 405 
gametes, 260-261 
gamma rays, 125, 145, 146 
Gamow, George (1904- ), 94, 129 
Gardner, E, 148 
gas: 

atmosphere, 170 

clouds, 83-84 

cold, 83 

gangrene organisms, enzyme, 221 

interstellar, 83 

isolating, 163, 164 

molecules, 122, 175 

pressure, 79 

specific gravity, 165 



gas: (cont.) 

terrestrial, 76 
gasoline, 180 
gastric juice, pepsin, 204 
Geiger counter, automatic record, 391 
general relativity, 33 
genes: 

artificially induced, 276 

bacteria, 267 

behavior, 264 

chemical nature, 266 

frequencies, 333 

functional interrelation, 273 

gene-complex, 265, 266, 271, 273- 
274, 276 

geographical restrictions, 333 

hereditary constitution, 258 

mapping genetic system, 266, 268 

molecular weight, 267 

mutation, 259, 265 

new, effect of, 334 

organization, 267 

recessive mutant, 275 
Genesis, myth of creation, 271 
genetics, 257-271 

analysis, quantitative, 332 

biological, 285 

effect of cultural beliefs, 337 

evolutionary implications, 256 

genetic drift, 334 

mutations, 267 

outbreeding, 276 

raising desirable qualities, 286 

variation, two kinds, 269 

see also evolution 
Genetics, Principles of (Sinnott and 

Dunn), 262 fn., 263 fn. 
Genghis Khan (1167-1227), 287 
geographical distribution, 273 
geology: 

inorganic chemistry, 178 

physical principles, 103 
geometry: 

astronomical space, 31-33 

atomistic school, 29-30 

elliptic, 34 

hyperbolic, 34 

irrational numbers, 28 

large-scale regions, 88 fn. 

logic, place in, 25-27 

non-Archimedean, 37 

non-Desarguesian, 37 

non-Euclidean, 34-35 



472 Index 



geometry: (cont.) 

rational, 26-27 

rigorous, 38-39 

theorems, 37 

see also mathematics 
germanium, semi-conductor, 134 
Germany: 

experimental psychology, 299 

idealism, philosophy, 300 
Germer, Lester Halbert (1896- ), 

128 

giant calculators, 387-388 
gibbons, variation, 331 
glass, ancient knowledge of, 155 
Glauber, Johann Rudolf (1604-1670), 

161, 431 

glottochronology, 330 
glucogenic amino acids, 208 
glucose: 

alcohol, 181 

blood, 210, 211 

chemical changes, 200 

glycogen, 205 

katabolic breakdown, 216 

molecules, 203-204 

stored energy, 187 
glutamic acid: 

formula, 207 

molecules, 209 
glycerol, discovery, 165 
glycine, 208; formula, 207 
glycogen: 

carbohydrate, 204, 205 

molecules, 203 

production, 200 

stored in liver, 210 
glycogenolysis, 210 
glycolysis, 212, 217 
glycosuria, 211 

goal-seeking strategy, 405-406 
God, variety of meanings, 249 
Godel, Kurt (1906- ), 53 
Goethe, Johann Wolfgang von (1749- 

1832), 409; quoted, 158 
goiter, iodine lack, 257 
gold: 

atoms, 125-126 

medieval alchemy, 159 

symbol, 169 
Gold, Dr. Mitchell, 367 
Gold, Thomas, 64, 65 
Goldschmidt, Richard B. (1878- ), 
270 fn. 



gorillas, cranial capacity, 324 
Gorki, Maxim (1868-1936), 3 
government agencies, work of anthro- 
pologists, 354-355 
gravitation : 

constant of, 92 

Einstein theory, 33 

law of, 69, 74, 75 

Newton's theory, 67, 68 
gravitational mass, 430 
Greeks: 

alchemical reasoning, 158 

geometry, 25-26 

irrational numbers, 28 

language, Western science related to, 
351 

material universe, 35 

mathematics and physics, distinction, 
62 

natural co-operation, 247 

Ouroboros serpent, 183; illus., 184 

parallel axiom, 30 

proving of theorems, 24, 39 

psychology, 295 

quadratic equation, 46 

whole number, 27 
green leaves, plant, 186 
Gregory, James (1638-1675), 22 
Grimm's Laws, 347 
group habits, language reflection, 345- 

346 

group preservation, animal, 247 
group survival, 245, 246 
growth, living things, 235 
growth factors, 220 
Gulliver's Travels (Swift), 414 
Gumey, Ronald W., 98, 139 



H 



habits, inviolability of political and so- 
cial, 7 

Hahn, Otto (1879- ), 139 

hair, amino acids, 205 

Haldane, J. B. S. (1892- ), 255, 
274 

Hales, Stephen (1677-1761), 164 

halogens, 170 

Hamilton, Sir William Rowan (1805- 
1865), 21 

hand-axes, 324 fn. 

haploid gametes, 260, 261 



Index 473 



Hardy, Sir Godfrey Harold (1877- 

1947), 20 

Hartman (psychoanalyst), 378 
Hawkins, Thomas, 435 
H-bombs, manufacture, 15 
heat: 

energy, 215 

enzymes, 202 

hydrocarbons, 188 

principle of the maximum, 236 
heath hen, extinction, 245 
heavy hydrogen, 103 
Heisenberg, Werner (1901- ), 98, 

133 
helium : 

atomic structure, diag., 171 

electrons, 127 

energy, 139 

hydrogen conversion, 78, 80, 95 

nuclei, 135, 141, 148, 174 

symbol, 169 
Helmholtz, Herman L. von (1821- 

1894), 295, 304 
hemoglobin, composition, 201 
hemophilia, 265 
Henderson, Lawrence (1878-1942), 

237 
hens, social orders of dominance, 243, 

244 

Henshaw antigen, 333 
herbalist, change to pharmacist, 160 
herbivorous animals, 218 
heredity: 

basis for scientific theory, 260 

chromosomes, 261 

mechanism, 256, 267 

or environment, 259 

primary function, 258 

self-reproducing gene-units, 266 

uniform, 259 

variations, effect on cultures, 337 
Hcrtzsprung-Russell diagram, 71, 80 
Hesse, R., 230 
hetcrocyclic ring systems, 185; diag., 

186 

heterogenesis, 274 
hidden parameters, 60 
Hilbcrt, David (1862-1945), 53; 

quoted, 102 

Hippocrates (460?-?377 B.C.), 218 
historical anthropology, 352 
Hitler, Adolf (1889-1945), 299 
Hobbcs, Thomas (1588-1679), 372 



Hodge, W. V. D., 22 
Hollerith, Dr. H., 401 
hominids, fossil, 273 
homo sapiens, see man 
homocyclic ring systems, 185 
homologous series, organic compounds, 

179-180 

hook orders, cows, 244 
Hooke, Robert (1635-1703), 106 fn^ 

162 
Hooton, Earnest A. (1887-1954) 

317 

Hopi Indians, language, 351 
Hopkins, Sir Frederick Gowland (1861* 

1947), 219 
hormones: 

carcinogenic, 223 

diabetogenic, 210, 211 

discovery, 222 

formation, 200 

natural organic compounds, 188 

sex, 223 

synthetic production, 201 
Homey, Karen (1885-1952), 378 
horses: 

fossil evidence, 280 

molars, pattern, 283 

stabilized, 280 
horseshoe crab, reaction to light, 238, 

240 

hostility, role, 371 
Hoylc, Fred, 64 
Hubble, Edwin Powell (1889-1953), 

32 

Huggins, Sir William (1824-1900), 21 
human: 

affairs, rate of change, 285 

biology, comparative, 330-337 

evolution (Washburn), 321-322 

existence, philosophical and anthro- 
pological problems, 378, 379 

life, recent changes, 6 

organs, association with planets and 
metals, 155 

sciences, progress, 16 

values, variability, 343 
Human Relations Area Files, 340 fn. 
humans, see man 

hunting, collective, Paleolithic Age, 324 
Huxley, Julian (1887- ), 235, 254- 

255 

Huxley, Thomas Henry (1825-1895), 
254, 281; quoted, 'ill 



474 



Index 



Huygens, Christian (1629-1695), 106 

fn., 116 

hyperbolic geometry, 34 
hydrocarbons, 179-182, 185, 188 
hydrogen : 

acceptor, 203 

atom, 127; diag., 171 

atomic number, 126 

atomic \\eight, 168 

created matter, 93 

deuterium, 135 

earth, early atmosphere, 232 

fused to form helium, diag., 432 

heavy, 103, 135 

inflammable air, 165 

interstellar, 83 

isotopic form, diag., 173 

material of stars, 76, 79 

molecules, 174, 175, 178 

nucleus, 129, 135-136 

symbols, 168 

transmutation, 78, 80, 95, 135, 139, 
234 

valency, 175, 176 
hydrogen chloride, discovery, 164 
hydrogen peroxide, 167 
hydrolysis: 

acid, 215 

digestive, 203 

processes, 202 
hydroxy-ethane, 181 
hyperon, particles, 149 
hypnosis, state of dissociation, 367 
hypotheses, chemistry, 155 

I 

iatrochemistry, 160 

ice, dimmed stars, 83 

iceberg, conscious and unconscious 

comparison, 365 
id and ego, conflict, 373 
idealism, philosophy, 300 
ideas, language shaper of, 351 
imaginary quantities, 45 
inbreeding, 276 
Inca civilization, 328 
India: 

four elements theory, 155 

judgment of guilt, 309 
individual evolution, 272 
Indo-European language: 

laryngeals, 348 

statistics available, 350 



induction, test, 433-434 
industrial anthropology, 354 
Industrial Revolution, 9, 386 
inertia, energy content, 114 
inertial mass, 430 
infant prodigies, 409 
infants, language, 347 
infinitesimal calculus, 62 
inflammable air, 165 
information : 

communication, 388 

entropy, 424-426 

organization, 420-426 

system, 424 

theory, 426 

infrared radiations, 103, 117 
inheritance: 

acquired characters, 258 

blending, 274 

cytoplasmic, 261 

environmental effects, 272 

instinct, 233 

mechanism, 271, 284 

mendelian, 261-264 

particulars, 266 

results of will and effort, 272, 274 

tendencies, 240 

see also evolution 
inner psychophysics, 298 
inorganic chemistry, 178 
inorganic scctoi, evolutionary process, 

278-279 
insanity, dreaming while awake, 367- 

368 
insects: 

breathing mechanism, 283 

restriction of evolutionary possibili- 
ties, 284 

stick, 385 

insight and foresight, 427 
instinct, inherited, 233 
instinctive behavior, 240-241 
instinctual wishes, unconscious, 373 
insulin, 210, 211, 430 
integral calculus, 394 
intellectual honesty, maintaining, 251 
intelligence, concept, 312 
intelligence tests, 313 
intensity, weakening with distance, 74 
interbreeding: 

humans, 331, 332, 334 

incompatibility, 270 
interferometer, 109, diag. 



Index 475 



intergalactic space, evolutionary proc- 
ess, 278 

internal-combustion engine, 386 
international agencies, work of anthro- 
pologists, 354-355 
international relations: 

based on war, 251 

use of anthropology, 355 
interpersonal relations, 379; linguistic 

uses, 346 fn. 
interstellar gas, 83 
intonation patterns, mental disorders, 

345 

intoxication, alcohol, 368 
introspection: 

behavior, 300, 301 

method, 299 
intuition, dangers, 37-38 
intuitionists, mathematics and logic, 55 
ion: 

atom, 137 fn., 171 

shifting location, 234 
ionic compounds, 177 
Iraq, stratigraphy sites, 325 
iron, symbol, 169 

irrational numbers, 27-28, 39, 43-44 
Isaiah (prophet), quoted, 186 
isobutane, 180 

isolationism, archaeological, 327 
isomeri/.ation, 203 
isomcrs, 180 
isotopes, 135, 139, 173 
isotropic space, 108 fn. 
Italy, cubic equation, 46 



j 



Jacob, prenatal influence, 257 
James, William (1842-1910), 309 
Java man, cranial capacity, 324 
Jeans, Sir James Hopwood ( 1 877-1946) , 

20 

Jefferson, Thomas (1743-1826), 409 
Jericho, stratigraphy site, 325 
Johnson, Samuel (1709-1784), 22, 197 
Jung, Carl J. (1875- ), 376 



Kant, Immanuel (1724-1804), 38, 52, 

300 

Kapitza, Peter L. (1894- ), 15 
Kardiner, Abram, 378 



katabolism, 200, 214, 216, 217 
Kekute, Friedrich August (1829-1896), 

185, 191, 192, 193; quoted, 179, 

183 
Kelvin, Lord (William Thomson) 

(1824-1907), 21, 35 
Kepler, Johannes (1571-1630), 67, 102 
ketogenic amino acids, 208 
ketone bodies, 211, 212 
ketonuria, 211 
kev, energy, 142 
kidney disease, diagnosis, 198 
killing prohibition, understanding, 345 
kinetic energy, 129 
kinship terms, 336 
Klein, Felix (1849-1925), 21 
Kluckhohn, Clyde (1905- ), 316- 

318 

knots, topology, 35 
knowledge: 

disinterested pursuit, 15 
fear of, 12 
Krebs, H. A., 213 
Kris, Ernest (psychoanalyst), 378 
Kroeber, Alfred Louis (1876- ), 

340 
Kiilpe, Oswald (1862-1915), 298, 299, 

310 



lactic acid, forms, 191; didg., 192 

lactic dehydrogenase, 203 

Lagrange, Joseph Louis (1736-1813), 

166 
Lamarck, Chevalier de (1744-1829), 

258, 271, 387 

land vertebrates, extinction, 281 
language: 

change, orderliness, 347 

culture paradigm, 346, 347, 350 

dating, 329 

epistemological, 351 

linguistic community, 346 fn. 

logical relation system, 350 

patterns, 351 

reflection of group habits, 345 

scientific study, 349-350 

social stratification, 346 fn. 

sound classes, 336 

Larmor, Sir Joseph (1857-1942), 21 
laryngeals, 348 fn. 
latency period, 370 



476 Index 



Lattes, C. M. G., 148 

Lavoisier, Antoine L. (1743-1794), 

163, 165, 166 

law, evolutionary study, 272 
Lawrence, Ernest (1901- ), 139 
lead: 

medieval alchemy, 159 
symbol, 169 
leaders, social rank, 244 
learning: 

experimental study, 307 
measurements, 296 
leather, ancient knowledge, 155 
Le Bel, Joseph Achille (1847-1930), 

190, 192 
Leibniz, Gottfried W. von (1646- 

1716), 48, 391, 429 
Lemaitre, Abb6 Georges Edouard 

(1894- ),94 

Le"mery, Nicolas (1645-1715), 160 
length measurements, space, 111-112 
Lenin, Nikolai (1870-1924), 3, 287 
Leucippus, 166 
lexico-statistic dating, 330 
liberty, limitations, 10-11 
libido: 

general psychic energy, 377 
sexual energy, 370, 379 
Liebig, Baron Justus von (1803-1873), 

quoted, 158 
life: 

basic facts, 275 
definition, 235 
drive for, 371 
early kind, 234 
environment fitness, 237 
nature of, 267 
origin, 231-235 
possibilities realized, 284 
produced on other planets, 279 fn. 
studies, 256 
tactics and strategy, 377 
temperature of existence, 237 
unicellular level, 279 
Life, The Facts of (Darlington), 257 

fn. 

Life Force, 272 
light: 

colored, wave length, 117 
corpuscular theory, 115-117, 121- 

122; diat>., 116 
diffraction, 117; illus., 118 
emission and absorption, 122, 126 



light: (cont.) 

intensity, 121-122; tropical forest, 

239 

nature, 103 
night sky, 93 
passage through rectangular opening, 

illus., 120 

passage through slits, diag., 119 
production, 215 
quantum, 103, 122, H5 
reactions to, 237-238 
receding source, 89 
rectilinear propagation, 74 
signals, velocity of propagation, 113 
speed, 114 
stars, 70-73, 76, 77, 78, 80-81, 85, 

87; diag., 86 

velocity, 86, 88, 89, 90, 96 
wave-particle duality, 121, 127 
wave theory, 108 110, 115-116, 118- 

119, 121; diag., 117 
likeness between things, 427 
lime, slaked, 182 
linguistics, 319 

anthropological, 346, 352 
evolutionary study, 272 
see also language 
linkage, genetic law, 268 
literature, scientific, 194 
lithium : 

symbol, 169 

transmutaton, 135, 139 
Littlewood, J. E., 21 
liver: 

carbohydrate storage, 204 
glycogcn, 210 
living matter: 
genetics, 256 

material transmission, 257 
lizards: 

collecting, 239 
fight orders, 244 
territorial defense, 243 
Lockyer, Sir Joseph Norman (1836- 

1920), 21 
Lodge, Sir Oliver (1851-1940), 21; 

quoted, 106 fn. 
logarithmic scale, 424 
logarithms, Napier invention, 389 
logic: 

and adaptation, 413-414 
deductive, 433, 434 
place in geometry, 25-27 



Index 



477 



logic: (cont.) 

symbolic, 48-50, 54 

see also mathematics 
logic of science, 427-436 

analysis into units, 428 

code, implication, 430 

experiments, use of, 432 

induction, test, 433-434 

insight a - iid foresight, 427 

likeness, 427 

units, finding, 429-430 
logical calculus, 48 
logical machines, 435 
logical positivism, Vienna school, 300 
Lorentz, Hendrik Antoon (1853-1928), 

111 

Lorentz-Fitzgerald concept, 112 
loyalty to human race, 14 
lubricating oils, 180 
luck, role in human life, 341 
Lucretius (96?-55 B.C.), quoted, 194 
luminiferous ether, 115 
luminosity, sun, 77 
luminosity-temperature diagram, 71 
Lysenko (scientist), 272 
lysine, formula, 207 
Lyttleton, R. A., 64 

M 

Mach, Ernst, 303 
machines: 

adaptive, 405-414 

deductive, 388-404 

evolution, 386 

experience in, 407-412 

exploring, 412-413 

game-playing, 406-407, 409 

injury, adaptation to, 413 

logic, 400-404 

procedures, diag., 395-398 

substitution for human labor, 9 
Maclaurin, Colin, 22 
macroevolution, 270 fn. 
macromoieculcs, 189 
macromutation, 270 fn. 
maggots, meat, 257 
magic, Paleolithic Age, 324-325 
magnesium, symbol, 169 
magnetic field, stars, 81 
main sequence stars, 71-72, 76-81 
maize: 

early production, 328 



maize: (cont.) 

zein, protein, 207 
males, territorial defense, 243 
maltase, enzyme, 204 
maltose, starch, 204 
mammalogy, 232 
mammals: 

dominance on land, 281 

higher, divergent specialization, 280 

territorial defense, 243 
man: 

activation, 296 

apelike ancestors, 272 

basic inner forces, 379 

behavior, science of, 355 

central cravings, 379 

cerebral cortex, 308-309 

common characteristics, 235 

co operative drives, 248 

cultures, identical values, 344 

dominance orders, 244 

domination, 385 

entry into New World, 326 

environmental control, 385 

evolution, 282, 288-289, 321-322, 
330, 352 

extermination, 6, 7, 8, 13 

fine perception, 302 

foresight, 427 

freak of nature, 379 

genes, number, 267 

heat output, 78 

history, 322-330 

ideological divergence, 287 

interdependence, 247, 340 

introspection, 300 

long-range task, 289 

modem, cranial capacity, 324 

modern, first appearance, 323 

needs, 311-312 

olfactory capacity, 302 

overspeciali7ed, 331 

peoples, constancies and variations, 
357 

single unit, 287 

striving, main source, 377 

stultifying effects of society, 380 

variation, 331-332 

virtues, biological basis for, 251 

visual space perception, 303 
manufacturing industries, dependence 

on chemistry, 178 
marble, heated, 163 



478 Index 



marine forms, separate sexes, 246 
Marx, Karl (1818-1883), 363 
Maseres, Francis (1731-1824), 47 
mass, nature, 430 

mass-energy relation, 136, 138, 145 
mass-luminosity, stars, 72; diag., 73 
mass protection, 245 
mass spectograph, 136; diag., 137 
material-spiritual relation, 294-295, 314 
maternal impressions, 257, 261 
mathematical physics, 106 
mathematicians, the first, 24-25 
mathematics, 24-62 

astronomical space, geometry, 31-33 

atomistic school, solid geometry, 29- 
30 

axioms, new views, 36-37 

electric discharges, opposite, 142 fn. 

electromagnetism, 111 

imaginary quantities, 45-47 

intuition, dangers, 37-38 

intuitionists, 55 

irrationals, discovery, 27-28 

logic, place in geometry, 25-27, 48- 
52, 415 

mathematicians, first, 24-25 

non-Euclidian geometries, 34-35 

numbers, 40-42 

numeration, system, 47-48 

paradoxes of Zeno, 28-29 

parallel axiom, 30 

Peano's symbolism, 50-51 

philosophy, 61-62 

physical chemistry, 178 

probability, 55-58 

quantum mechanics, 102, 132 

relativity, general, 33 

rigorous geometry, 38-39 

Russell's paradox, 53-55 

short cuts, discovery, 394 

space time, 39-40 

statistics, 58-59 

stochastic systems, 60 

symbolic logic, 48-50 

three-dimensional space, 45 

topology, 35-36 

transfinite numbers, 42-45 

ultimate realities, 173 

Whitehead-Russell developments, 51- 

53 
matter: 

aggregation, 156 



matter: (cent.) 

atomic constitution, 166-167 

continual creation, 93 

discontinuous, 166 

extended substance, 298 

four elements, diag., 156 

granular structure, 349 

heat and thermal properties, 103 

law of conservation, 167 

living and nonliving, 235 

mind, association with, 155 

nature, 154 

study, 154 

unity, 158, 194 

wave and probability properties, 103 
mauveine, 184, 185 
maximum, principle, 236 
Maxwell, James Clerk (1831-1879), 

111 

Maya pottery, wheel-made, 327 
Mayow, John (1641-1679), 162, 164 
Mayr, Ernst, 278 

measurement and observation, psychol- 
ogy, 296 

measurements, space and time, 111-112 
meat, maggots, 257 
mechanical aptitude, 313 
mechanical energy, 215 
mechanics, laws of, 113 
mechanism, life studies, 256 
medicine: 

chemistry applied to, 160 

cultural anthropology, applications, 
354 

physical anthropology, contributions, 

353 

medieval culture, 362 
medium-bright stars, 85 
meiosis, reduction, 260 
Meitner, Use (1878- ), 139 
memories, storing, 309 
memory test, reaction times, 306 
men, the ways of, 338-345 
Mendel, Abb< Gregor Johann (1822- 

1884), 261, 264, 268, 273 
Mendel, Lafayette Benedict (1872- 

1935), 207 
Mendel6eff, Dmitri Ivanovich (1834- 

1907), 169, 170 

mendelian inheritance, 261-264, 273 
Mendel's laws, 268 
Menninger Clinic, 374 



Index 479 



mental disorders: 

connection with social norms, 342 

speech aid in diagnosis, 345 

therapy, 373 
mental health, 379-380 
mental phenomena, measuring, 295 
mental philosophy, 295 
mental possibilities, advance, 284 
mercaptan, 302 
mercury: 

chemical and mystical significance, 
160 

symbol, 169 

Mercury (planet), orbit, 33 
mercury-sulphur theory, 158, 160 
Mesoamerica, archaic horizon, 328 
Mesolithic Age, 325 
mesons: 

particles, 143 

summarized, 148 

Mesozoic, reptilian supremacy, 281 
message symbols, checking, 423 
metabolic changes, enzymes, 201 
metabolism : 

abnormalities, 210 

amino acids, 212 

bacterial, 220, 224 

carbohydrate, 205, 209, 210-213 

derangement of normal, 222 

diabetic subjects, 210-212 

energy, 214-218 

fat, 210-213 

nitrogen, 206 

protein foods, 205-210 

summary of main lines, diag., 212 
metallurgy, inorganic chemistry, 178 
metals: 

alkali, 170 

ancient knowledge, 155 

association with human organs and 
destinies, 155 

burning, 163 

photoelectric effect, 122-123 

sulphur-mercury theory, 158 

transmutation, 159 
mctaiuathcmatics, 53 
methane (marsh gas): 

earth, early atmosphere, 232 

formulae, 176 

model, 191; diag., 192 

molecular, 174 

paraffin series, 180 



MEV, million electron volts, 129, 145 
Mexico, National University, psycho- 
analytic training, 376 
Mexico, pre-Columbian horizon, 327 
mice: 

fight orders, 244 

spontaneously generated, 257 
Michelson, Albert Abraham (1852- 

1931), 109 fn. 
Michelson-Morley experiment, 109, 

111, 112; diag., 109 
Michurin, J. V., 272 
Micrographia (Hooke), 162 
microorganisms: 

nutritional requirements, 219-220 

pathogenic, checking, 223, 224 

unicellular, 277 
microscope, electron, 144 
microscopy, 198-199 
mileage counter, 391 
military, aided by constitutional anthro- 
pology, 353 
milk: 

importance in diet, 219 

souring organisms, 220 
Milky Way, 81, 83 
Miller, Stanley, 231 
Millikan, Robert Andrews (1868-1953), 

145 
mind: 

and behavior, 272 

brain, interaction, 298 

matter, association, 155 

self-reproduction, 285 

uncxtended substance, 298 
mines, ventilation, 390 
minimax strategy, 417-419 
minimum, principle of, 2>6 
mitochondria, particles, 199 
mitosis, 260 
Mittag-Lefflcr, G., 21 
models, astronomers', 67, 75-76 

Abb6 Lemaitre, 94 
modern alchemy, 1 57 
modifications of the individual, 259 
molecular formula, 169, 175 
molecules: 

atom combinations, 174 

Avogadro's hypothesis, 175 

behavior, 104 

changes, 175 

compound atoms, 167 



480 



Index 



molecules: (cont.) 

configuration, 190, 191; diag., 192 

deamination, 209 

energy-content, 188 

food digestion, 203, 214 

gas, 122 

genes, 267 

glucose, 200, 203-204 

glutamic acid, 209 

ions, shifting location, 234 

lifelike, 231, 232 

light-emitting properties, 134 

multiple, 190 

natural organic, 186 

nitrogenous part, 208 

rearrangement, 203 

simple, 190 

standard patterns, 189 

structure, 193 

superfluous amino-acid, 209 

symmetry, 191-193 

tetrahedral angle, 192 

weight, 175 
monkeys: 

high-ranking males, 244 

territorial defense, 243 
monocyclic ring systems, 185; diag., 186 
monomer, simple molecule, 190 
Monroe Doctrine, anthropological, 326, 

327 

moon, 69 
Morley, Edward Williams (1838- 

1923), 109 jn. 
morphological structure, exploration, 

198 

morphology, 232, 256, 273 
Morse Code, 386 
mortality tables, 133 fn. 
moths, melanic, 275 fn. 
motion: 

Einstein's equations, 114 

laws of, 115, 429 

Newtonian view, 114 
motivation, 298, 299, 306, 310-312 

dynamic psychology, 297 

unconscious, examples, 364-365 
motor reaction, 306 
mule, interbreeding, 270 
Muller, Hermann Joseph (1890- ), 

265, 276 

multiple proportions, law, 167 
muons, summarized, 148 
Murdock, G. P., 340 



Murray, Henry Alexander, 317 
muscles: 

carbohydrate storage, 204 

enlargement, 257-258 

enzyme, 215 

protein, necessity for, 206 
mustard gas, mutations, 277 
mutation: 

artificially induced, 265 

discovery, 265 

genes, 259, 267 

hereditary material, 273 

inexact copying, 269 

new hereditary traits, 333 
mythology, expression of human wis- 
dom, 377 

myths, interpersonal relations stabiliz- 
ing, 341 



N 



naphthalene, formulae, 184 
Napoleon I (1769-1821), 287 
national planning, problems, 399 
national statistics, 400 
nationalistic development cycles, 339 
nationality, liberal doctrine, 10 
natural: 

co-operation, 244 

organic compounds, 179, 188 

philosophy, 295 

selection, 246, 247, 271-276, 280, 

281, 286, 334, 363 
Natural Selection, Genetical Basis of 

(Fisher), 266, 274 
nature: 

based on mathematical plan, 173 

understanding, 428 
Navaho, kinship terms, 336 
navigation, study of astronomy, 386 
Nazism, morally acceptable, 343 
Neanderthal Man, 323; cranial ca- 
pacity, 324 

Near East, planned food raising, 325 
near stars, 84 
Neddermeyer, S., 148 
need and attitude concept, 311 
negative numbers, 46 
Negroes, African, serological genes, 333 
Neolithic Age, 325-326 
neon: 

atomic structure, dt'dg., 171 

symbol, 169 



Index 



481 



neoprene, molecules, 190 
nerve-muscle components, behavior 

complex, 240 
neurosis, 374 

neurotic character, 373-374 
neurotic symptoms, artistic creation, 

377 

neutretto, 149 

neutrino, 141-142; summarized, 147 
neutron : 

atomic nucleus, 105 

catalyst, 160 

code, 431 

discovery, 103, 135 

summarized, 146-147 
New Mexico, cave cultures, 328 
New Political Arithmetick, 399-400 
Newlands, John (chemist), 169, 172 
Newton, Isaac (1642-1727): 

atom, 167 

gravitation theory, 33, 67 

light, corpuscular theory, 116 

mechanics, laws of, 113-114, 115, 
127 

metal transmutation, 159 

motion, laws of, 102, 429, 430 

philosophy, 62 

solar system, work on, 68-69 
nicotinic amide, 222 
Nietzsche, Frieclrich Wilhelm (1844- 

1900), quoted, 365 
night blindness, 218 
night sky, darkness, 88, 93 
Nile, riv. Africa, flooding, 386 
Nirn, game, 407; dwg., 408 
nineteenth century, degree of repres- 
sion, 372 

nip orders, fish, 244 
nitric oxide, 168 
nitrobenzene, 185 
nitrogen : 

atom, valency, 175 

food cycle, 187 

protein source, 206 

symbols, 168, 169 

transmutation, 174 

nitrogen-rich soils, excessive growth, 257 
nitrogenous equilibrium, 206, 207, 208 
nitroglycerine, 188 
nitrous gas, symbols, 168 
noisy line, 421-423 
non-Archimedean geometry, 37 
non-Desarguesian geometry, 37 



non-Euclidean geometries, 34-35 
nonluminous matter, dimmed stars, 8 
nonpolar bond, covalency, 176 
normal behavior, predictable, 345 
normal butane, 180 
nose, smelling sensitivity, 302 
nose form, cold climates, 335 fn. 
noughts-and-crosses machine, 406 
novocaine, 189 
nuclear atom: 

model, 126 

structure, 103 
nuclear energy: 

power, main source, 8 

reaction, 77 

scale, 391 
nuclear fuels, 386 
nuclear particles, wave theory, 129 
nuclear physics, 103 
nuclear pile, 387 

nuclear reactions, 77-78, 138; code, 431 
nuclear research, 144 
nucleic acid, chemical template, 266 
nucleon, 140; summarized, 146 
nucleus: 

analyzed into unit concepts, 431 

cohesive forces, 140 

distance between parts, 391 

positive and negative electrical units, 

171 
number-squaring machine, procedure^ 

394; cfmg., 395-398 
numbers: 

atomic, 135 

cardinal, 41-42 

irrational, 27-28, 39, 43-44 

negative, 46 

ordinal, 41 

rational, 42 

real, 44 

transfinite, 42-45 
numeration, system, 47-48 
nylon, macromolecules, 190 



O 



oat seedlings, reaction to light, 238 
object constancy, 304 
obscurantism, fighting, 14 
observable phenomena, 362-363 
observation, instruments, 387 
observation and measurement, psychol- 
ogy, 296 



482 Index 



obstetricians, contributions of physical 

anthropology, 353 
octaves, law of, l'69, 172 
octonory system, numeration, 47-48 
Oedipus complex, 370 
Ohm, Georg Simon (1787-1854), 389 
Ohtsuki, Dr. Kenji, 378 
oil, exhaustion, 8 
Olbers, Ileinrich (1758-1840), 84 
assumptions, 85-94 
paradox, 87, 88, 89, 92; diag., 86 
olefiant gas (cthylene), symbols, 168 
Ommaney, Erasmus, 21 
ontogeny, 272 
obgenesis, diag., 263 
open-chain compounds, 183 
open-chain structures, 185 
oppositcs, pairs, 157 
optical phenomenon, content, 108 
optically active organic matter, 191, 193 
optimum, principle of, 236 
order, axioms, 36 
ordinal numbers, 41 
organic chemistry: 
"Big Four," 179 
biochemistry, 199 
division of chemistry, 178 
molecular, 186 
organic compounds, homologous series, 

179 

organic compounds, natural, 188 
organic defects, psychological signifi- 
cance, 377 
organic energy, 188 
organic explosives, 188 
organic materials, radioactive disinte- 
gration, 329 
organic molecules: 
structure, 179 
tetrahedral angle, 192 
organisms: 
diverse, 279 
earliest, 279 
genetic mechanism, 267 
living, evolution, 232 
living, similarity, 199 
lower, co-operation, 244 
oxygen intolerant, 236 
self- reproducing chromosomes, 261 
organization: 
in a code, 426 
main steps, 286 
rise in level, 279 



organization: (cont.) 

simple types, 233 
organization and information, 420-426 

information and entropy, 424-426 

information in a system, 424 

noisy line, 421-422 

organization in a code, 426 

redundancy, 423 

signal and noise, 420 
organs, disuse, 257 
Origin of Species (Darwin), 272 
orthogenesis, 272, 274 
orthopedic surgeons, contributions of 

physical anthropology, 353 
Osborne, Thomas Burr (1859-1929), 

207 

osteomalacia, 221 

Ouroboros Serpent, 183; illus., 184 
ova, 260 

overcrowding, dangers, 245 
oxaloacetate, 214 
oxidation: 

biological, 201, 203 

chemical change, 182 

fat, 214 
oxide, 163 
oxygen : 

atom, valency, 175 

discovery, 164-165 

first production, 236 

nitrogen transmutation, 174 

symbols, 168, 169 

vital need, 311 



Paleolithic Age, 323-324, 329, 330 
paleontology, 272, 273, 277 
-aminobenzoic acid, 221, 224 
pancreas: 

amylase, 203 

insulin, 210 
pangenesis, 259 fn. 
pantothenic acid, 222 
Paracelsus, Philippus Aureolus (1493?- 

1541), 160 
paradox: 

Olbers', 87, 88, 89, 92; diag., 86 

Russell's, 53-54 

paraffin hydrocarbons, 180, 181, 192 
paraffin wax, 180 
parallel axiom, 30-31, 34, 37 
parasites, modern viruses, 234 



Index 483 



parent relationships, 369 

parental attitudes, effect on personality, 

343 

Park, O., 230 
Park, T., 230 
parthenogenesis, 269 
particles: 

atomic physics, summarized, 145-149 
behavior, H2 
electrical, 104 
light, theory, 116, 121 
mechanics, 129 
subccllular, 199 
velocity, 79 

particulate inheritance, 266 
Pascal, Blaise (1623-1662), 55, 391, 

415; quoted, 414 
Pascal-Leibniz machine, 391 
Pasteur, Louis (1822-1895), 166, 190, 

191, 430; quoted, 193 
patterns, standard molecular, 189 
Pauli, Wolfgang, 79, 147 
Pavlov, Ivan Pctrovich (1849-1936), 

307 

Peano, Giuseppe (1858-1932), 3; sym- 
bolism, 50-51 
pebble tools, 322, 323 
peck orders, birds, 244 
pediatrics, growth study contributions, 

353 

Peking man, 323; cranial capacity, 324 
penicillin, 223 
penicillium, mold, 277 
Pennsylvania, petroleum, 180 
pepsin, enzyme, 204 
peptidascs, enzymes, 204 
perception, 304-305 
perfect cosmological principle, 85 fn., 

91, 92-93,94, 95, 96 
perfumes, natural organic compounds, 

188 

periodic table of elements, 169 
Perkin, Sir William Henry (1838- 

1907), 183, 185 
Perkin's mauve, 184 
perpetual motion machine, 274 
personal equations, 305 
personality, influence of culture, 342- 

343 

personality type, 380 
personnel problems, anthropological 

techniques, 340 
petro-chcmicals, 185 



petroleum : 

derivatives, 188 

hydrocarbons, 180, 183, 185, 188 
pharmacist, herbalist's change to, 160 
pharmacology, 222 
phenol, formulae, 184 
phenomena, recurring, 107 
philosopher's stone, 158, 159 
philosophical principles, languages built 

on, 350 
philosophy: 

function, 248 

libidinal forces, 372 
Philosophy, International Congress of, 

Paris (1900), 3, 51 
phlogiston, 163, 166 
phonemes (sound classes), 336, 348, 

348 fn., 349 
phosphate, enzyme-catalyzed reaction, 

216 

phosphorus, symbols, 168, 169 
photoelectric cell, 386 
photoelectric effect, light emission and 

absorption, 122-123, 126 
photography, light, 238 
photon quantum, 145 
physical anthropology, 319, 335, 353 
physical chemistry, 178 
physical constants, 92 
physical sciences, 154; experimental 

data, 399-400 
physical types, human, recognizable,. 

332 
physicists: 

analyzing experiment records, 431 

work in two worlds, 105 
physics, 102-149 

atomic, 79, 134-144,415 

atoms, 125-131 

light, 115-125 

major discoveries, 103 

mathematical, 106 

motion, 108-115 

Gibers' assumption, 85-92 

particles, atomic, summarized, 145- 
149 

terrestrial, 67-75 

wave mechanics, 131-134 
physiological chemistry, 198 
physiological genetics, 266 
physiological psychology, 295, 296 
physiology, 232 

evolution of, 272 



484 Index 



physiology (cont.) 

organic chemistry, 178 

studies in, 256 

physique-behavior relation, 335 
pigeons, learning, 296, 308 
pigments : 

formation, 200 

natural organic compounds, 188 

retinal, 221 

synthetic production, 201 
pilot, automatic, 409, 412, 413, 422 
pions, summarized, 148 
piperidine ring, diag., 186 
pituitary gland, 210 
plague, spread throughout Eastern 

Hemisphere, 16 

Planck, Max (1858-1947), 103, 145 
Planck's constant, 123 
planets: 

association with human organs and 
destinies, 155 

motion, 67 

outer, living matter on, 237 
plants: 

animal-plant relation, 236 

behavior patterns, 240 

change in unfavorable surroundings, 
245 

continuous transformation, 274 

domestication, 325, 326 

genetic mechanism, 267 

green, leaves, 186 

green, synthesis, 218 

group stabilization, 282 

intercrossing, 270, 276 

light, reactions, 237 

mutation, 265 

one-celled, 235 

polysaccharides, 205 

proteins, amino acids, 207 

separate species, 279 
platinum black, catalyst, 202 
Plato (4277-347 B.C.), mathematics, 

173 

play, animals, 405 
pneumatic trough, 164 
Poincare', Jules Henri (1854-1912), 21 
polar bond, electrovalency, 176 
political behavior, affected by science, 

16 

political philosophy, changes in, 9 
political systems, libidinal forces, 372 



politicians, professional skill, 12 
politics, psychoanalytic knowledge, 379 
polonium, interaction with alpha par- 
ticle, 130-131 

polycyclic ring systems, 185; diag., 184 
polymer, multiple molecule, 190 
Polynesian languages, sound classes, 336 
polyploidy, chromosome-doubling, 276 
polysaccharide, 205 
polysaccharide glycogen, 200 
polythene, molecule, 189 
Pope, William Jackson (1870-1939), 

152 
population: 

constant average, 95 

differentiation, 334 

distinctive human problem, 288 

effect on evolution, 246-247 
positron-electron, 142 
positron, generation and annihilation, 

143 

positron, summarized, 146 
posture, adopting upright, 331 
potassium, symbol, 169 
pottery, early production, 328 
Powell, C. F., 104 
power, striving for, 377 
power-hungry machines, 386 
power-stations, atomic, 10 
power tools, 386-387 
pragmatism, 300 
predisposition, 306 
pressure, compressed matter, 79 
pressure, stellar matter, 76 
Priestley, Joseph (1733-1804), quoted, 

164-165 

primary needs, 311 
primitive concepts, mathematics, 39 
Principia Mathematica (Whitehead 

and Russell), 52, 53 
principle, cosmological, 85 fn., 91, 92-93 
principles, three, diag., 194 
printing, invention, 285 
printing press, 387 
probability, theory of, 55-58, 415 
process, explaining, 428 
process, life studies, 256 
production levels, maintaining, 9 
productive orientation, 379-380 
progress, resistance to, 9 
propane, formulae, 180 
properties, galaxies, 96 



Index 485 



prosthetic group, protein, 201 
proteins: 

amino acids, 204, 205, 206, 232 

animal, 208-209 

carbohydrate, 213 

daily requirement, 206 

energy providing, 186 

enzymes, 201 

fat, 213 

foods, function and metabolism, 186, 
205-210 

gene-units of heredity, 266 

insulin, 222 

macromolecules, 190 

nitrogenous equilibrium, 206, 207, 
208 

oxidation, 214 

plant, 208 

protoplasm, living, 232 

synthetic production, 201 

tissue building, 186, 205 
proto-co-operation, 233, 244; animals, 

247 

proton-electron pairs, 171 
protons: 

atomic nucleus, 105, 126 

behavior, 104 

code, 431 

scattered, 129 

summarized, 146 
protoplasm, growth and destruction, 

235 

protoplasm, living, protein, 232 
protozoans, 235 

evolution, 246 

learned behavior, 242 
protozoology, 232 
psychic energy, transforming, 380 
psychoanalysis, 362-380 

Asiatic philosophic concepts, 378 

neo-Freudian theories, 378-380 

theory, 364-373 

therapy, 373-376 

psychoanalyst, objective observer, 377 
psychic juice, saliva secretion, 307 
Psycholinguistics, 349 fn. 
Psychological Association, American, 

300 

psychologists, handling of psychic dif- 
ficulties, 376 
psychology, 294-314 

ability, 312-313 



psychology (cont.) 

emotion, 309 

learning, 307-309 

motivation, 310-312 

perception, 304-305 

psychophysics, 301-304, 314 

reaction, 305-306 
psychophysics, 301-304, 314 
Psychophysics, Elements of (Fechner), 

295 

psychoses, 374, 378 
psychosocial evolution, 284-289 
psychosomatic diseases, 378 
Ptolemy, Claudius, model, 67 
Pueblo Indians, classic civilization, 328 
puffers, alchemists, illus., 158 
pyridoxal, 222 
pyrrole, ring, diag., 186 
pyruvate, 213, 222 
pyruvic acid, 212 
Pythagoras, 26, 27, 28, 44 



quadrant, 387 
quadratic equation, 46 
qualitative chemistry, 164, 165, 177 
quantum : 

energy, 145 

mechanics, 102, 129, 131-133 
quartz, atoms, 124 

quicklime, chalk decomposition, 163, 
164 



R 



rabbits, color- types, 267 

race mixture, 334 

race prejudice, witchcraft substitute for, 

341-342 

races, major human, 333 
radio waves, interstellar gas atoms, 8B 
radioactive clouds, 13 
radioactive elements, 125 

measuring disintegration, 328 
radioactivity: 

barrier leakage, 134 

spontaneous, 77 
radiography, X-ray quanta, 145 
radiometer, 302 
radium : 

atom, spontaneous breakup, 60 



486 Index 



radium: (cont.) 

radiations, 125 

radioactivity, 129, 173 
Rank, Otto (psychoanalyst), 377 
rare-earth elements, 172 
rational geometry, 26-27 
rational numbers, 42 
rationalization, concept, 365-366 
rats: 

appearance changes, 264 

diet experiments, 219 

future lies with, 7 

introspection report, 300 

learning ability, 299, 308 

visual brain areas removal, 309 
raw materials: 

allocation, 10 

dependence on chemistry, 178 

exhaustion, 7-8 

Rayleigh, Lord (1842-1919), 21 
reaction, nuclear, 77-78, 138, 431 
Read, Arthur Hinton, 153 
Read, John (1884- ), 152-153 
real numbers, 44 
reasoning, alchemical, 158 
reciprocal proportions, law of, 167 
red-displacement, spectrum, 33 
Red Star, The, 1 3 
red stars, 71,72, 80, 81 
red shift, spectra of galaxies, 91 
Redi, Francesco (16267-1697?), 257 
reduction, chemical change, 182 
redundancy, 423 
relatives, categories, 336 
relativistic cosmology, 92 
relativity: 

cultural, 343 

general, 33 

theory, 40, 90, 93-94, 103, 108, 113, 

127, 274, 430 
religion : 

contribution of anthropology, 341 

evolutionary study, 272 

expression of human wisdom, 377 

learning from science, 248-249 

libidinal forces, 372 

scientifically oriented, 233 
repressed ideas, time reactions, 306 
repressed wishes, 297 
repressions, sublimation, 371 
reproduction : 

incompatibility, 270 

living beings, 235 



reproduction: (cont.) 

sexual, 260 

reptilians, extinction, 281, 282 
resistance, concept, 365 
resonance, nuclear reactions, 138 
restriction of evolutionary possibilities, 

283 

retina, human, sensitivity, 302, 304 
rhesus monkeys, high-ranking males, 

244 

riboflavin, 220, 222 
rickets, 221 

rigorous geometry, 38-39 
ring-atoms, 185; diags., 184, 186 
ring-systems, 185, 192 
rituals, stabilizing interpersonal rela- 
tions, 341 

rocks, age estimate, 107-108 
rocksalt, atoms, 124 
rod, measuring, contraction in motion, 

111 

Rohheim, Geza (psychoanalyst), 378 
rubber, natural and synthetic, 189-190 
Rubner, Max (1854-1932), 206, 208 
Russell, Bertrand (1872- ), 2-5 

mathematical developments, 51-53 

paradox, 53-54 

Rutherford, Ernest (1871-1937), 15, 
21, 103, 125-126, 157,171, 173 



Saccheri, parallel axiom, 31, 32 
sage grouse, high-ranking males, 244 
Sahara desert, rain, 10 
saline conditions, succulence of plants, 

257 

saliva secretion, psychic juice, 307 
salivary amylase, enzyme, 202, 203 
salt: 

chemical and mystical significance, 
160 

salivary amylase cof actor, 202 
salts, formation, 170 
Sanskrit languages, sound system, 347 
Sapir, Edward (1884-1939), 349 fn. 
saturated substances, 181 
scale of values, 419 
Sceptical Chymist, The (Boyle), 162 
Scheele, Karl Wilhelm (1742-1786), 

quoted, 165 

schizophrenia, 374, 378, 379 
Schmidt, K. P, 230 



Index 



487 



Schrodinger, Erwin (1887- ), 98, 

103, 128 

Schuster, Sir Arthur (1851-1934), 21 
science: 

analytic method, 429 

association with war, 1 5 

Chinese lack of development, 351 

continuous refinement of calcula- 
tions, 415 

liberator, 17 

logic, 427-436 

of leftovers, 320 

procedure, 429 

religion learning from, 248-249 
Science, British Association for the Ad- 
vancement of, 14 
science as foresight, 385-436 

adaptive machines, 405-414 

deductive machines, 388-404 

organization and information, 420- 
436 

strategy and its safeguards, 414-419 
Science Awakening (Van der Waer- 

den), 27 fn. 

sciences, experimental, 433 
scientific age, 314 
scientific knowledge, dangers, 16 
scientific revolution, 17th century, 161 
scientific theories, purpose, 67, 73 
scientists, social duty, 11-17 
scurvy, deficiency disease, 218 
sea-urchin eggs, divisions, 246 
secret code deciphering, linguistic anal- 
ysis, 352-353 

seeds, exposure in a vacuum, 236 
segregation, genetic law, 268 
selection, culture influences, 334 
self-assertion, anarchic, 11 
self-preservation, animal, 247 
self-reproduction, mechanism, 267 
self-transformation, 286 
semi-conductors of electricity, 134 
Semitic language, statistics available, 

350 

sensations, difference between intensi- 
ties, 294-295 
sense-physiologists, 296 
senses, thresholds, 301-302 
sensory discrimination, improvement, 

258 
sensory perceptions, linguistic patterns, 

351 
sensory reaction, 306 



separate species, formation, 280 

servomechanisms, 412 

sex: 

chromosomes, 260 fn. 

genetical knowledge, 269 

hormones, use of, 223 
sexual : 

choice, social laws, 340 

desire, physiological need, 311 

reproduction, 260 

strivings, 370 
shadow, light theory, 116; dmgs., 116, 

117 
Shakespeare, William (1564-1616), 

409 
Shaw, George Bernard (1856-1950), 

272, 423 

Sheldon, W. H., 335 
shift, Doppler, 70 fn. 
shortfall, 422 
Shortley, George H., 98 
Siberia, fertility, 10 
sibling relationships, 369 
signal-to-noise ratio, 420-421 
silicon : 

basis for life, 237 

semi-conductor of electricity, 134 

symbol, 169 
silver: 

medieval alchemy, 159 

symbol, 169 

similar processes, theory, 412 
similarity in figures, 26 
Simpson, George Gaylord, 278 
Sino-Tibetan language, statistics avail 

able, 350 

sins, seven capital, 251-252 
size constancy, 304-305 
size variation, human stature, 264 
skin, amino acids, 205 
slavery, morally acceptable, 343 
sleep: 

dissociation, 366 

vital need, 311 
slide rule, 389 

slim figure, acquisition, 204-205 
smoking, process of rationalization, 365 
snakes, evolution, 281, 282 
soap, ancient knowledge, 155 
social anthropology, evolutionary study, 

272 

social life, adhesions of certain feature^ 
340 



488 Index 



social organization, 340, 341 

social peck order, animals, 244 

social psychology, 297 

social relations, needed changes, 16 

social science, problems, 399 

social stratification, linguistic usages, 

346 fn. 

social structure, changes, 340 
social systems, determination, Marx's 

theory, 363 
sociality, animals, 233 
socially patterned defect, 380 
society, interdependence, 9-10 
socioeconomic structure, role, 380 
sociology, psychoanalytic knowledge, 

379 
sodium : 

atomic structure, diags., 171, 172 

symbol, 169 
sodium hydroxide (caustic soda), 170, 

177, 182 

sodium ion, dzdg., 172 
sodium nitrate and water, equation, 

177 

soil, exhaustion, 7, 8 
solar system, see astronomy; stars; sun 
solid geometry, atomistic school, 29-30 
solids: 

elastic, 106, 107, 108 

electrical properties, 134 
somatypes, 335 
souls, transmigration, 271 
sound: 

change, 347, 349 

classes (phonemes), 336, 348, 348 
fn., 349 

speed, 393 

South America, early population, 326 
space: 

absolute motion in, 110 

astronomical geometry, 31-33 

homogeneity and isotropy, 108 

measurements, 111, 112 

popular notions, 336 

theory, 190, 191, 193 

three-dimensional, 45 

time, 39-40 

spagyric chemistry, 160 
spatial visualization, 313 
species: 

extinction, 245 

origin of new from old, 269 



species: (cont.) 

related, separate biological entities, 

270 

specificity, enzymes, 202 
spectrograph, mass, 136, dfdg., 137 
spectroscope, 386 

inferences, 74 

value, 70-71 
spectrum : 

light emitted by atoms, 127 

red displacement, 33 

wave lengths, 121 
speech : 

discovery, 386 

information conveyed by, 345 

true, 284 fn. 

see also language 
spermatogenesis, diag., 263 
spermatozoon, 260 
sperms, 260 

Spinoza, Baruch (1632-1677), 364 
spiral galaxies, 81; illus., 82 
spiritualistic philosophy, 314 
spiritual-material relation, 294, 295, 314 
sponges, mass protection, 245 
spontaneous generation, 259 
spontaneous mutation, 265 
spores, exposure in a vacuum, 236 
spread of discoveries, 338-339 
squaring a number, machine procedure, 

394; d/dg., 395-398 
stabilization, evolutionary, 280-284 
Stahl, Georg Ernst (1660-1734), 163 
starch: 

green chlorophyll, 232 

maltose, 204 

molecules, 203 

photosynthesis, 236 

production, 200 

stored energy, 187 
starchy food, digestion, 202 
stars: 

age, 80 

binary, 69 

blue, 71, 81 

bright, 72, 80, 84 

changes, 75 

constitution, 69-70, 73, 75, 76, 80 

dimmed, 83 

faint, 71, 72, 80, 85 

fixed, 66 

galaxies, 66, 95 



Index 489 



stars: (cont.) 

gravitational forces, 76 

interaction with gas and dust, 84 

life history, 272. 278 

light, 69, 70-73, 76, 77, 78, 80-81, 
85, 87; didg., 86 

line-of-sight velocity, 70 

magnetic field, 81 

main sequence, 71-72, 76-81 

measurement, dmg., 70 

medium bright, 85 

near, 84 

origin, 84 

partially dimmed, 83 

receding, 432 

red, 71, 72, 80, 81 

structure, 74-76 

sub dwarf, 81 

surface area, 71 

temperature, 71, 72, 76-77, 78, 79 

velocity, 86, 89 

white/71, 72, 80 

yellow, 71 

starvation, nitrogen, 206 
states, limitations on liberty, 10-11 
statesmen, duty, 16 
statistical accounting, 399 
statistics, theory of probability, 58-59 
steam-driven machines, 386 
stereochemistry, 193 
stereoscopic color vision, 276, 321 
stereoscopic movies, 3-D perception, 

304 

sterile hybrid, 276 
Stern, Otto, 129 
Stevenson, E. C., 148 
stick insect, 385 
stilbestrol, 223 
stochastic systems, 60-61 
stock ticker, 386 
Stokes, Sir George Gabriel (1819-1903), 

21 

Stone A